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PSYC Exam 2 (ch.8-)
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Terms in this set (267)
CH 8: 2-37
CH 12: 38-73
CH 13: 74-
*start of each ch. is starred
A null hypothesis is rejected when
b. the probability of finding a difference that large if the population means are equal is very low.
Sometimes we reject the null hypothesis when it is true. This is technically referred to as
a. a Type I error.
If we were to repeat an experiment a large number of times and calculate a statistic such as the mean for each experiment, the distribution of these statistics would be called
c. the sampling distribution.
A two-tailed test is _______ powerful than a one-tailed test if we are sure the difference is in the direction that we would have predicted.
b. less
In the finger tapping example in the text ("Using the Normal Distribution to Test Hypotheses" in Chapter 8), we would reject the null hypothesis when
b. the patient tapped too slowly.
A Type II error refers to
d. failing to reject a false null hypothesis.
One of the problems we face when we try to draw conclusions from data is that we have to deal with
b. error variance.
The _______ assumes all means are equal for a given measure?
d. null hypothesis
If the data are reasonably consistent with the null hypothesis, we are likely to
c. retain the null hypothesis
When we are willing to reject the null hypothesis for any extreme outcome, we are making a
a. two-tailed test.
A Type I error concerns
a. the probability of rejecting a true null hypothesis.
If we erroneously conclude that motorists are more likely to honk at low status cars than high status cars, we
d. both a and c
Dr. Harmon expected that her neurotic patients would come significantly earlier to all scheduled appointments compared to other patients, and planned to run a one-tailed test to see if their arrival times were much earlier. Unfortunately, she found the opposite result: the neurotic patients came to appointments later than other patients. What can Dr. Harmon conclude from her one-tailed test?
d. Neurotic patients did not come to appointments significantly earlier than other patients.
Which of the following is most likely to represent a statement of the null hypothesis?
d. H0 : μ = 0
The hypothesis that we are trying to support by running an experiment is often called
d. the research hypothesis.
Which of the following pairings is correct?
a. Type I; Type II:: α; β
Another name for a one-tailed test is a
a. directional test.
Another name for sampling error is
d. both a and b
We are more likely to declare two populations to be different if
a. the means of our samples are very different.
Whether or not we reject the null hypothesis depends on
d. all of the above
We are most likely to reject a null hypothesis if the test statistic we compute is
b. quite extreme.
Rejecting a true null hypothesis is known as
d. both b and c
The area that encompasses the extreme 5% of a distribution is frequently referred to as
b. the rejection region
The sampling distribution of the mean that you saw in the text
a. resembled a normal distribution.
The value of the test statistic that would lead us to reject the null hypothesis is called
a. the critical value.
To reject a null hypothesis for the finger tapping example in the text ("Using the Normal Distribution to Test Hypotheses" in Chapter 8), we would
b. calculate the probability of that result if the null hypothesis were true.
By convention, we often reject the null hypothesis if the probability of our result, given that the null hypothesis were true, is
b. less than .05.
A researcher was interested in seeing if males or females in large lecture classes fell asleep more during in-class videos. The null hypothesis of this study is
c. males and females fall asleep at the same rate.
The standard deviation of a sampling distribution is known as
a. the standard error.
The basic reason for running an experiment is usually to
a. reject the null hypothesis.
The probability of NOT rejecting a FALSE null hypothesis is also known as
a. Type II Error
To look at the sampling distribution of the mean we would
c. calculate many means and plot them.
The difference between a test comparing two means and a test comparing the frequency of two outcomes is
a. the test statistics that they employ and their calculation.
After running a t-test on the mean numbers of jelly beans that men and women eat over the course of the year, I conclude that men eat significantly more jelly beans than women. If men and women actually eat the same number of jelly beans, my conclusion is
b. a Type I error
The basic idea behind hypothesis testing
c. is largely the same across a wide variety of procedures.
Sampling distributions help us test hypotheses about means by
c. telling us what kinds of means to expect if the null hypothesis is true.
If we have calculated a confidence interval and we find that it does NOT include the population mea
d. this will happen a fixed percentage of the time.
A 95% confidence interval is going to be _______ a 99% confidence interval.
a. narrower than
When we are using a two-tailed hypothesis test, the null hypothesis is of the form
d. H0 : μ = 50.
Cohen's d is an example of
c. a d-family measure.
The reason why we need to solve for t instead of z in some situations relates to
c. the sampling distribution of the variance.
In using a z test for testing a sample mean against a hypothesized population mean, the formula for z i
d. none of the above
The confidence intervals for two separate samples would be expected to differ because
d. all of the above
I want to test the hypothesis that children who experience daycare before the age of 3 do better in school than those who do not experience daycare. I have just described the
d. all of the above
When are we most likely to expect larger differences between group means?
b. when there is very little variability within groups
When you have a single sample and want to compute an effect size measure, the most appropriate denominator is
b. the standard deviation of the sample.
The term "effect size" refers to
c. the actual magnitude of the mean or difference between means.
It makes a difference whether or not we know the population variance because
d. we have to call the result t if the sample variance is used.
If we have run a t test with 35 observations and have found a t of 3.60, which is significant at the .05 level, we would write
c. t(34) = 3.60, p <.05.
When you are using a one-sample t test, the degrees of freedom are
b. N - 1.
The t distribution
c. approaches the normal distribution as its degrees of freedom increase.
If the population from which we sample is normal, the sampling distribution of the mean
c. will be normal.
If we knew the population mean and variance, we would expect
d. the sample mean would differ from the population mean by more than 1.96 standard errors only 5% of the time.
If the standard deviation of the population is 15 and we repeatedly draw samples of 25 observations each, the resulting sample means will have a standard error of
b. 3
The standard error of the mean is a function of
d. both b and c
In one-sample tests of means we
b. compare one sample mean against a population mean.
An assumption behind the use of a one-sample t test is that
a. the population is normally distributed.
A one-sample t test was used to see if a college ski team skied faster than the population of skiers at a popular ski resort. The resulting statistic was t.05(23) = -7.13, p < .05. What should we conclude?
a. The sample mean of the college skiers was significantly different from the population mean.
Which of the following does NOT directly affect the magnitude of t?
d. The population variance (σ2).
The point of calculating effect size measures is to
b. convey useful information to the reader about what you found.
All of the following increase the magnitude of the t statistic and/or the likelihood of rejecting H0 EXCEPT
d. a smaller significance level (α).
When are we most likely to expect larger differences between group means?
b. when there is very little variability within groups
The sampling distribution of the variance is
a. positively skewed.
The standard error of the mean is
c. the standard deviation of the sampling distribution of the mean.
A confidence interval computed for the mean of a single sampled.
d. is associated with a probability statement about the location of a population mean.
In one-sample tests of means we
b. compare one sample mean against a population mean.
With a one-sample t test, the value of t is
d. positive if the sample mean is larger than the hypothesized population mean.
A t test is most often used to
a. compare two means.
For a t test with one sample we
b. lose one degree of freedom because we estimate the population mean.
If we fail to reject the null hypothesis in a t test we can conclude
d. that we don't have enough evidence to reject the null hypothesis.
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The importance of the underlying assumption of normality behind a one-sample means test
b. depends on the sample size.
Which of the following statements is true?
d. Confidence limits are the boundaries of confidence intervals.
In a repeated measures t, the degrees of freedom are equal to
b. N - 1.
When we have related samples, the best measure of the effect size d^ uses
b. the standard deviation of the pretest scores (if they exist).
We would be least likely to use a repeated measures design when
b. there are minimal individual differences.
The standard error of the difference between two means is
b. the standard deviation of a set of means of difference scores.
Cohen's d refers to
d. the difference between the means before and after treatment divided by a standard deviation.
In the t test for repeated measures the symbol sD stands for
c. standard deviation of differences scores.
Suppose that we take 15 gay couples and observe the difference within couples in terms of age. Then we take 15 straight couples are record the same differences. We want to test if straight couples are more similar in age than gay couples. (There is some reason to expect that this is true.) What statistical procedure would be most appropriate?
b. running an independent samples t test between gays and straights
We want to study the mean difference in autonomy between first-born and second-born children. Instead of taking a random sample of children we take a random sample of families and sort the children into first- and second-born. The dependent variable is a measure of autonomy. This experiment would most likely employ
a. a repeated measures analysis.
Which of the following is sometimes a serious problem with repeated measures designs?
a. Carryover effects can cloud the interpretation.
If two sets of measures have the same mean, but different variances, the resulting t will be closest to
c. 0.00
A repeated measures t test is more likely to lead to rejection of the null hypothesis if
d. the degree of change is consistent across subjects.
Which of the following was NOT an advantage of repeated measures designs discussed in the text?
c. It is easier to calculate the statistics.
The null hypothesis of a related scores t test is
a. µD=µ1-µ2=0
We are evaluating a method of therapy for extremely underweight adolescent girls. If we weighed our subjects at the beginning and end of therapy, a difference in weight could mean
d. all of the above
As the value of the mean difference score decreases
b. the t score decreases.
Which of the following terms does NOT belong with the rest?
c. independent samples
If the effect of the first measurement influences what the subject does on the second measurement, we would name this
b. a carryover effect.
The mean of a column of difference scores is equal to
b. the difference between the means of the individual columns.
In the Kaufman and Rock (1972) moon illusion example in the text, they hypothesized that there would be no moon illusion in their experiment. Experiments of this type pose problems for researchers because
a. you cannot logically prove the null hypothesis to be true.
The t test for two related measures
b. is simplified by the fact that we really only focus on the column of difference scores.
A difference score is obtained by
d. either a or b, just so long as you are consistent
The difference between the values of degrees of freedom for one sample t tests and related means t tests is that
c. related means t tests have a df = N - 1, where N is the number of pairs of scores.
The null hypothesis in a repeated measures t test is
a. the hypothesis that the mean difference score is equal to 0.
An experimenter collected data on how well a study guide improved grades on an exam taken late in the semester compared to an exam taken early in the semester. Using a related sample means t test, the results showed that later grades were higher than early grades (t(74) = 3.64, p < .05). Which of the following was NOT an advantage of this design?
c. The design controlled for carry-over effects from already having taken one exam when the second exam was administered.
A chess team advisor wanted to examine how long it took his top two players, Fishy Bobber and Chet Mate, to complete their moves. Over the course of 50 matches each, Fishy averaged 330 seconds to move while Chet averaged 420 seconds to move. If the overall standard deviation for Fishy and Chet was 45 seconds, what was the effect size of their difference?
c. 2.0
When we have an independent sample t test, the degrees of freedom are equal to
c. N1 + N2 - 2
The statistical test that compares two or more means is a(n)
c. ANOVA.
A weighted average is
b. an average that gives greater influence to the larger sample.
Which of the following formulae for t is correct?
d. all of the above
We would NOT pool the variances if
d. we had very unequal sample variances.
Using the conservative test in which variances were not pooled that was described in the text, on how many degrees of freedom would the t test on groups of 65 and 21 participants be based?
b. 21 - 1 = 20 df
Which of the following is a reason why we may NOT find a significant difference between two groups?
d. all of the above
In which of the following cases is it most useful to pool the variances?
c. s12 = 8.4, N1 = 13 and s22 = 12.1, N2 = 19
The following data are taken from Chapter 14 and refer to a study of weight gain in treated and untreated girls suffering from anorexia. In the anorexia example comparing Family Therapy and Control conditions the null hypothesis would be
a. μFT = μC
The following data are taken from Chapter 14 and refer to a study of weight gain in treated and untreated girls suffering from anorexia.Which of the following formula for t in this situation would be a correct one?
b. t=-0.45-7.26/√(63.82/26)+(51.23/17)
Which of the following would most likely NOT be independent samples?
a. Group 1 contains wives and Group 2 contains their husbands.
When variables A and B are independent, the variance of A - B is equal to
a. the variance of A plus the variance of B.
The reason that we pool variances is to
b. get a better estimate of error variance.
For a very conservative test when we don't pool the variances we should
c. use a much reduced number of degrees of freedom.
When testing the means of independent samples, the null hypothesis is best thought of as
a. the mean of population 1 is equal to the mean of population 2.
The most important characteristic of two independent samples is
c. the set of scores for one sample is uncorrelated with the scores in the other sample.
Our assumption that population variances are equal is called the assumption of
c. homogeneity of variance.
One of our best aids in handling problems of non-normality is
b. the central limit theorem.
The normality assumptions behind the independent groups t test
d. diminishes in importance as the sample sizes increase.
For a very conservative test when we don't pool the variances we should
c. use a much reduced number of degrees of freedom.
When we have very unequal sample variances, we should
b. not pool the variances.
When testing the means of independent samples, the null hypothesis is best thought of as
a. the mean of population 1 is equal to the mean of population 2.
An important reason for using random assignment in a study with independent groups is to
d. a and c
EXAM 3 Ch16
XX
The column of mean squares in the analysis of variance is obtained by
a. dividing the sums of squares by the degrees of freedom.
You want to control the _______ when multiple comparisons are being made?
c. familywise error rate
A researcher found significant differences in the mean running speeds of sprinters wearing shoes made by Nike, Reebok, and Adidas using an analysis of variance. The η2 calculated on the basis of group membership (based on which shoes were worn) equaled .16. The value of η2 shows that
c. 16% of the variability in running speed is attributed to shoe brand.
The notation nΣ(x̄ j - x̄..)^2 is used to calculate
a. SSbetween
In the analysis of variance, MSerror is
d. the average of the within group variances.
In the analysis of variance, MSGroups measures how different group means are, and MSerror measures variability within each group. If the null hypothesis were false, what would we expect to find?
b. That MSgroups would be larger than MSerror.
When looking at multiple comparisons, the more tests that you run, the more likely that you will have a _______.
a. Type I error
The analysis of variance compares
c. the variance between group means with the variance within groups.
The book discusses an experiment by Merrell that examined the effects of Anthrax, Mozart, and no music on the amount of time it took a mouse to run a maze. To determine if there is an overall difference between the three groups, Merrell ran an ANOVA. To determine which means differed for each other, he ran a
c. Bonferroni test.
When we use the phrase "within group" we mean
c. the variability calculated for the scores within each group separately.
The analysis of variance assumes that
c. the populations have equal variances.
An important assumption in the one-way analysis of variance is that
b. observations are independent.
We use the symbol s2/x to represent
d. the variance of the means.
The analysis of variance differs from a t test for two independent samples because
d. both a and b
In evaluating the F in the analysis of variance, we need to know
d. both a and b
The mean square error (MSerror) is a measure of
c. how much variability there is within each group.
Mean squares are closest to
b. variances.
When we speak about error variance in the analysis of variance we are speaking of
a. differences between subjects in the same group.
We generally don't compute a confidence interval on the omnibus null hypothesis because
d. all of the above
If we want to have faith in the results of our particular study, we will be most concerned with
b. random assignment.
For an F value to be significant it must
c. exceed the tabled value.
Which of the following represents a measure of the magnitude of effect?
d. all of the above
In multiple comparison procedures, post-hoc tests are completed after the ANOVA. Why are post-hoc tests preferred over running several t-tests?
a. They decrease the probability of a Type I error.
The Bonferroni procedure controls error rates by
a. operating at a reduced level of α.
In the analysis of variance with three groups the null hypothesis is
c. the three population means are equal to each other.
What type of multiple comparison procedure should be used if we want to divide the familywise error rate among the number of comparisons that we are performing?
b. Bonferroni procedure
When we reject the null hypothesis in the analysis of variance we can conclude that
c. at least one of the means is different from at least one other mean.
In the Eysenck study of recall of lists of words, a significant F in the analysis of variance would at the least tell us that
c. the recall means are different in the different groups.
Which of the following is a possible null hypothesis in an analysis of variance with 5 groups?(H1: µ1 ≠ µ2 ≠ µ3 ≠ µ4 ≠ µ5; H2: µ1 ≠ µ2 = µ3 = µ4 = µ5)
d. Neither of these is a null hypothesis.
The null hypothesis behind a simple multiple-group analysis of variance is of the form:
c.µ1=µ2=µ3=µ4
The familywise error rate is
a. the probability of at least one Type I error.
Which of the following is not a critical element of the analysis of variance?
c. the variance of the total sample
In evaluating the F in the analysis of variance, we need to know
d. both a and b
If the null hypothesis is true, we would expect the F in the analysis of variance to be
b. somewhere around 1.
A student wanted to determine if the mean number of times a student missed class was different for sophomores, juniors, and seniors. After collecting attendance data, the student ran an ANOVA and found that MSgroups was much larger than MSerror. This student can conclude that
b. there is a difference in the mean number of times sophomores, juniors, and seniors miss class.
The major difference between t tests and the analysis of variance is that the latter
a. deals with multiple groups.
When we use the phrase "omnibus null hypothesis" we are referring to
b.µ1=µ2=µ3=µ4
The notation Σ(X - ..)2 produces the term we call the
c. SStotal
In an analysis of variance summary table, the df for groups always equals
b. the number of groups minus one.
We want to compare the scores of different groups on a measure of reaction time. Three different groups were studied: patients with recent head injuries, patients with old head injuries, and a control group of non-injured people. We want to know which group of people has the fastest reaction time. What is the best statistical test to use to find this out?
a. one-way ANOVA
If we had the following pattern of population means (μ1 = μ2 = μ3 ≠ μ4) we would hope to conclude that
a. the null hypothesis is false.
The notation Σ(X - x̄..)2 produces the term we call the
c. SStotal
In the analysis of variance, the more the null hypothesis is false,
a. the larger the value of F.
If we run six independent comparisons among means, each at the five percent level, the overall familywise error rate will be approximately
c. .30.
Ch. 17
XX
The notation x̄.. stands for
d. the grand mean.
If you have a significant interaction, you should
a. think carefully about any main effects you might have.
In the factorial design analyses discussed in Chapter 17, the different cells
c. always have different subjects.
Which of the following is not an advantage of factorial designs over one-way designs?
c. They make it easier to deal with unequal sample sizes.
Dr. Gates looked at the effects of frustration on the use of profanity by males and females. Males and females were asked to write a lab report on computers in a lab, but half the computers were set up to crash during the session while half of the computers were not set up to crash. Three observers recorded the use of profanity by the participants during the task. What is the design of this study?
a. 2 x 2 factorial
In the Spilich et al. study of the effects of smoking that was discussed in the text, active smokers were found to do better than nonsmokers on a driving task but did worse than nonsmokers on a cognitive task. However, over all three tasks (the third was pattern recognition and the groups were not different on that) active smokers did not differ from nonsmokers on performance. The results suggest
b. an interaction between smoke group and task, but no main effect for smoke group.
The overall effect of an independent variable is called a(n)
a. main effect.
Which of the following is NOT true in a factorial analysis of variance?
a. SStotal = SSA + SSB + SSAB
The degrees of freedom for an interaction in a two-way factorial are equal to
c. the product of the degrees of freedom for the main effects.
Use the following research scenario to answer question:
A researcher was interested in the effects of 1) alcohol consumption and 2) content of a videotape, on how likely one is to support rape myths. The researcher randomly assigned 60 college-aged males to one of the following three groups: no alcohol consumed, a moderated amount of alcohol consumed, and a large amount of alcohol consumed. Additionally, half of the participants were shown the educational video on rape myths. The other half of the participants watched a documentary on owls (a control condition). At the end of the study all the participants filled out a survey on rape myth acceptance. Higher scores on the survey indicated higher acceptance of rape myths.
How many cells does this experiment have?
c. 6
To calculate the F for a simple effect you
a. often use the same error term you use for main effects.
To calculate the magnitude of effect estimates for a factorial design, the methods are
b. simple extensions of the methods used with a one-way design.
_______ are the effect of one variable at one level of the other variable.
a. simple effects
To calculate the F for a simple effect you
c. use the same error term you use for main effects.
Use the following research scenario to answer the question:
A researcher was interested in the effects of 1) alcohol consumption and 2) content of a videotape, on how likely one is to support rape myths. The researcher randomly assigned 60 college-aged males to one of the following three groups: no alcohol consumed, a moderated amount of alcohol consumed, and a large amount of alcohol consumed. Additionally, half of the participants were shown the educational video on rape myths. The other half of the participants watched a documentary on owls (a control condition). At the end of the study all the participants filled out a survey on rape myth acceptance. Higher scores on the survey indicated higher acceptance of rape myths.The results indicated that the participants who watched the educational video scored significantly lower on the rape myth scale compared to the group that watched the owl video.
What does this suggest?
b. There is a main effect of video type.
In a factorial analysis of variance you cannot have
d. Any combination is possible.
When you compare the effect of one variable at one level of another variable you are examining
b. a simple effect
To calculate the F for the interaction in an analysis of variance we
a. divide the MSinteraction by MSerror.
To calculate the sum of squares for a treatment effect in the analysis of variance, we would work with
a. the squares of the differences between the treatment means and the grand mean.
A simple effect is calculated by
a. looking only at the data for one level of one of the independent variables.
If you have a significant interaction,
c. at least one simple effect is likely, though not certain, to be significant.
The following is a printout from SPSS. From this table, which of the following conclusions would be wrong?
c. The interaction is significant.
A 2 × 4 factorial has
b. 2 levels of one variable and 4 levels of the other.
A factorial design has at least
c. two independent variables and one dependent variable.
In this graph we can see that there is
b. an interaction between location and time.
Unequal sample sizes in a factorial analysis of variance
a. are difficult to deal with when doing calculations by hand.
Pliner and Chaiken (1990) wanted to investigate whether the amount of food eaten depended on the gender of the participant and the gender of the confederate. It was observed that women eat less than men overall and that women eat less in the company of men than they do when in the company of other women. The finding that women eat less than men across all conditions is a(n)
d. main effect.
To look at an interaction effect we must
c. plot the data in such a way that we see how each independent variable changes at each level of the other independent variable.
Use the following research scenario to answer the question:
A researcher was interested in the effects of 1) alcohol consumption and 2) content of a videotape, on how likely one is to support rape myths. The researcher randomly assigned 60 college-aged males to one of the following three groups: no alcohol consumed, a moderated amount of alcohol consumed, and a large amount of alcohol consumed. Additionally, half of the participants were shown the educational video on rape myths. The other half of the participants watched a documentary on owls (a control condition). At the end of the study all the participants filled out a survey on rape myth acceptance. Higher scores on the survey indicated higher acceptance of rape myths.
If the analysis of variance is significant, we are pretty sure that
b. at least one mean is different from one or more other means.
Which of the following graphs is most likely to portray an interaction?
a. I
A simple effect is calculated by
a. looking only at the data for one level of one of the independent variables.
The main effect of a variable is
b. the effect of that variable averaged over the levels of other independent variable(s).
In a study which investigated the effects of amount of coffee consumption and mood (good or bad) on driving speed, the magnitude of effects estimates were as follows: Coffee: ; Mood: ; Coffee x Mood: . Together, how much of the variability in driving speed is accounted for by Coffee, Mood, and their interaction?
c. .51
A simple effect is defined as
c. the effect of one variable at a single level of the other variable.
ch. 9/10
XX
Which of the following is the formula for the covariance?
a. COVxy = E(x-x̄)(y-ȳ)/ N-1
If you drop a pencil randomly on a scatterplot, what aspect are you changing as you rotate the pencil about the point where it crosses the Y axis?
a. the slope.
The intercept of a regression line is
a. the value of ȳ when X=0.
In the equation for a straight line used in the text, the intercept is represented by
a. a
The correlation between two variables is defined as
a. the covariance of those variables divided by the product of their standard deviations.
If the correlation between X and Y is negative, the slope of the regression equation must be
a. negative.
If the correlation between the rating of cookie quality and cookie price is .30, and the critical value from the table of significance of correlation coefficients is .35, we would say that
a. the correlation is not significant
Which of the following is the most accurate statement?
d. Neither correlation nor R squared nor regression show causation.
A reliable correlation is one that
b. is likely to be closely approximated in a future study.
In plotting the relationship between the incidence of breast cancer and the level of vitamin D in the body, we would most like
c. vitamin D on the X axis and incidence of breast cancer on the Y axis.
The regression line always passes through the point
b. x̄, ȳ
The covariance measure is
c. the degree to which observations vary together.
The following is a scatterplot of data that my students collected concerning the relationship between the cost of chocolate chip cookies and their rated quality. The correlation between the two variables is most likely to be
d. .00
A curvilinear relationship is one in which
d. both b and c
If we want to specify the percentage of the overall variability in life expectancy attributable to variability in smoking behavior, the statistic we want to look at is
b. r2
When I want to make a prediction but don't have the value of X on which to base that prediction, my best estimate is
c. the mean of Y.
When we have considerable spread of the points about the regression line, the slope of that line will be _______ the slope of a similar line when there is less scatter.
c. the same as
A regression line is
c. the best fit straight line.
The covariance between height and running speed on the State College track team was equal to -28.21. This tells us that the
b. relationship between height and speed is negative.
If we do know X, our measure of error is
c. the standard error of estimate.
A newspaper headline writer found that the more adjectives she put in the titles of her articles, the greater the number of newspapers that were sold that day. This relationship between numbers of adjectives and newspaper sales must be
d. positive.
The correlation between amount of caffeine consumed and nervous behavior was found to be .30. What conclusion can be drawn from this finding?
b. 9% of the of the variability in nervous behavior can be accounted for by variability in amount of caffeine consumed.
Professor Falls wants to determine if there is a relationship between frequent hearing of a startle stimulus and hearing loss. He ran a regression and obtained an r value of .60. Which of the following best summarizes what this result means?
b. 36% of the variability in hearing loss can be accounted for by variability in the hearing of startle stimuli.
When the data are in the form of ranks we
b. can just apply the standard formula to the ranks.
The "best fitting line" is that regression line that
c. minimizes the sum of squared errors of prediction.
If the R squared between brain size and IQ is .09 then
c. 9% of the variability in IQ is accounted for by variability in brain size.
The symbols a and b are frequently referred to as
a. regression coefficients.
We can think of the standard error of estimate as
a. the standard deviation of the errors that we make when using the regression equation.
If you drop a pencil randomly on a scatterplot, what aspect are you changing as you move the pencil vertically on the page without rotating it?
b. the intercept.
In testing the significance of a correlation coefficient, the degrees of freedom are
c. N - 2
A significant correlation is one which
b. means that the variables are not linearly independent.
The notation SS stands for
d. sum of squares.
If the correlation between two variables is .76, and the sample size is large, we can conclude that
b. there is a strong positive relationship between the two variables.
An important thing about r2 is that it represents a measure of
b. accountable variability.
When the slope of the regression line is positive, the line goes from
b. lower left to upper right.
When we restrict the range of X or Y, we may
d. All of the above are possible
Which of the following represents a closer relationship between two variables?
d. r = -.65
The covariance will always
c. reflect the direction of the relationship.
If the correlation between X and Y is significant, that tells us
a. that the slope is significant.
If we do not know X, our measure of error in predicting Y is
a. the standard deviation of Y.
In the equation ȳ = 12.6 X + 5
d. a difference of one unit in X will lead to a 12.6 point difference in the prediction.
In calculating the regression coefficients we square the errors of prediction because
b. the sum of the errors would always be 0 for a great many lines we could draw.
Early in the correlation chapter the author showed figures in which he drew vertical and horizontal lines at the mean of each variable to cut the graph into four quadrants. When there is a high positive correlation between two variables, we would expect most of the data points to fall
b. in the upper right and lower left quadrants.
An example in the text hypothesized that 4% of the variability in life expectancy was accounted for by variability in smoking behavior. The values of r and r2, respectively, are equal to
a. .20 and .04.
When we use heterogeneous subsamples of data, such as older and younger subjects, the resulting correlation between intelligence and education could
d. all of the above
The example showing a negative relationship between speed and accuracy tells us that
c. on average, slower responders are more accurate than faster responders.
Which of the following pairs go together?
a. dependent variable : criterion variabl
When we say that the correlation between Age and test Performance is significant, we mean
c. the true correlation between Age and Performance in the population is not equal to 0.
Which r-value represents the strongest correlation?
c. -.75
The notation (Y - ȳ ) represents
d. error in prediction.
In plotting the relationship between the incidence of breast cancer and the level of vitamin D in the body, we would most likely plot
c. vitamin D on the X axis and incidence of breast cancer on the Y axis.
For the following data, ΣXY is equal to
d. 36
The equation for a straight line is an equation of the form
d. Y = bX + a
For a given set of data the covariance between X and Y is .80. The standard deviation of X is 2.0, and the standard deviation of Y is 3.0. The resulting correlation is closest to
b. .15
If we have a regression line predicting the amount of improvement in your performance as a function of the amount of tutoring you receive, an intercept of 12 would mean that
c. even without tutoring you will improve.
The correlation in the population is denoted by
a. ρ
If you want to plot the regression line, after having found the regression equation, you need to calculate ȳ for _______ value(s) of X.
c. a minimum of two
The notation ȳ is used instead of Y
c. to indicate that the result is a prediction.
The standard error of estimate is given by
d. none of the above
If high scores on X are paired with low scores on Y, the covariance is going to be
b. negative.
A regression analysis of hours spent exercising and ounces of weight loss had a slope of 3. We would predict that
a. for every 1 hour of exercise, a person would lose 3 ounces of weight.
In the equation for a straight line used in the text, the slope is represented by
b. b
When we use a regression equation to make a prediction, the errors that we make are often referred to as
a. residuals.
The data illustrated in the graph below suggest
c. that some other variable is involved in the relationship.
A correlation was computed between amount of exercise people do and people's overall happiness. A significant correlation was found, such that the more people exercise, the happier they are. What is the best conclusion to draw from this finding?
c. A positive relationship exists between exercise and happiness.
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Magnetic resonance imaging (MRI) is well established as a tool for measuring blood velocities and volume flows. The article “Correlation Analysis of Stenotic Aortic Valve Flow Patterns Using Phase Contrast MRI,”, proposed using this methodology for determination of valve area in patients with aortic stenosis. The accompanying data on peak velocity (m/s) from scans of 23 patients in two different planes was read from a graph in the cited paper. $$ \begin{matrix} \text{Level-} & \text{.60} & \text{.82} & \text{.85} & \text{.89} & \text{.95} & \text{1.01} & \text{1.01} & \text{1.05}\\ \text{Level--} & \text{.50} & \text{.68} & \text{.76} & \text{.64} & \text{.68} & \text{.86} & \text{.79} & \text{1.03}\\ \text{Level-} & \text{1.08} & \text{1.11} & \text{1.18} & \text{1.17} & \text{1.22} & \text{1.29} & \text{1.28} & \text{1.32}\\ \text{Level--} & \text{.75} & \text{.90} & \text{.79} & \text{.86} & \text{.99} & \text{.80} & \text{1.10} & \text{1.15}\\ \text{Level-} & \text{1.37} & \text{1.53} & \text{1.55} & \text{1.85} & \text{1.93} & \text{1.93} & \text{2.14} & \text{ }\\ \text{Level--} & \text{1.04} & \text{1.16} & \text{1.28} & \text{1.39} & \text{1.57} & \text{1.39} & \text{1.32} & \text{ }\\ \end{matrix} $$ a. Does there appear to be a difference between true average velocity in the two different planes? Carry out an appropriate test of hypotheses (as did the authors of the article). b. The authors of the article also regressed level-- velocity against level- velocity. The resulting estimated intercept and slope are .14701 and .65393, with corresponding estimated standard errors .07877 and .05947, coefficient of determination .852, and s = .110673. The article included a comment that this regression showed evidence of a strong linear relationship but a regression slope well below 1. Do you agree?
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Let U and V be independent random variables each having the standard normal density. Set $$ Z=\rho U+\sqrt{1-\rho^{2}} V, $$ where $-1<\rho<1$. (a) Find the density of Z. (b) Find the joint density of U and Z. (c) Find the joint density of $X=\mu_{1}+\sigma_{1} U$ and $Y=\mu_{2}+\sigma_{2} Z$ where $\sigma_{1}>0$ and $\sigma_{2}>0$. This joint density is known as a bivariate normal density. (d) Find the conditional density of Y given X = x.
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