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Final: Stats 311
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Key Concepts:
Terms in this set (142)
the correct order of operations in math is what?
PEMDAS
___is the variable that is believed to change in the presence of the independent variable
dependent variable
the scale of measurement a researcher uses
determines the type of inferential statistics that can be done
interval scales of measurement
have equidistant scales (they are distributed in equal units)
researchers measure data in a ______ to learn more about individuals in the larger _____of interest
sample;population
A therapist observes the spouses are more likely to forgive their partners for lying to them if they find out the truth from their spouses and a third party. the dependent variable is
forgiveness
each of the following is an example of quantitative data except:
weight in ounces
income in dollars
political affiliations
age in years
political affiliations
procedures that allow researches to infer or generalize observations made with samples to the larger population from which they were selected best describes
inferential statistics
a researcher records the time it takes to complete a memory task in a sample if 25 participant. he find that the average participation completed the test in 43 seconds. the average time to complete this task is called an?
sample statistics
a researcher compares the amount if college debt (in dollars ) that undergraduate students incur up to their 4 year degree. college debt is on what scale of measurement?
ratio
which of the following best describes an independent variable ?
the manipulated variable
which if the following best describes a dependent variable
the measurement behavior
bar charts are a lot like histograms except ?
the bars displayed in the graph do not touch
to construct a pie chart, first distribute the data as?
relative percentages
a simple frequency distribution:
a) can be used to summarize the grouped data
b)can be used to summarize ungrouped data
c)summarized the frequency of scores in a given category or range
d) all of the above
all of the above
A researcher wants to determine how many participants will take less than 24 seconds to complete a cognitive performance task. If he constructs a frequency distribution for these data. what type of distribution would be most appropriate to answer this question?
a cumulative frequency distribution from the bottom up
a cumulative percentage summary that indicates the percentages of scores at or below a given value is called a
percentile rank
a researcher finds that 12% of participation make between 3-5 visits to a physician each year . what are the real limits for this interval?
2.5-5.5
the mode is an appropriate measure of central tendecy for:
a)data that are bimodal
b)use w other measures of central tendency
c)data that are on a nominal scale
d)All of the above
all
the population mean is symbolized at ____ whereas the sample mean is symbolized as ____
U:M
a researcher reports that the average shopper in the sample (n=12) purchased $65.00 worth of items (U=$65.00) during a busy shopping day. what mistake was made in this citation?
the sample mean is written in the wrong notation
when would a researcher calculate a population mean?
when data are measured for all members of a population
a researcher records the following data for the number of dreams recalled during a night of sleep for 10 college students: 324431102 and 0. is the mean equal to the median in this example?
yes
the ____is the middle value in a distribution of scores that are listed in numeric order
median
a researcher records 52 scores. what is the median position if these scores
the average of the 26th and the 27th scores in numeric order
a researcher selects a sample if 6 males and 11 females. she ask the students to rate the likelihood they would do female stereotyped jobs...... what is the weighted mean for this entire sample of 17 participants?
3.5
a professor grades 120 participants papers and reports that the average score was an 80%. what do we know about the sum of the differences of these 120 scores from their mean of 80%
the sum of the differences is equal to zero
a researcher ask participants to estimate the height of a statue that was in a waiting area. the researcher records the following estimates 40 46 30 50 and 34. if the researcher removes the estimate of 40 then the value of the mean will____
remain the same
measures of variablilty cab range in value from
0 to +infinity
a measure of the average squared distance of scores from the mean is called the
variance
a researcher records the following data: 4 4 4 4 and 3. How would you describe the variability of those data
it is very small (close to 0)
regardless of the number of scores in a distribution the range only includes____scores in its calculation
2
a researcher decides to split scores on an exam into quadrilles she determines that a score of 64 is at the 25th per, 74 is at the 50th per, abd 80 is at the 75th per. what is the interquartile range for this data?
16
a researcher records the time in seconds it takes a sample of participants to walk alone through a dark portion of campus. the researcher computes SS=1,000. assuming that a sample of 11 participants was observed in this study. what is the standard deviation for these data
10 seconds
a researcher measures the number of trials it takes two samples of participates to master a new task. SS= 240. sample A consisted of 12 ppl. sample B consisted of 18 participants. which sample is associated with the largest variance
sample A
which is true about the computational formula for variance?
all of the above
each deviation in the numerator for variance is squared because
without squaring each deviation, the solution fir SS would be zero
68% of classes were between 68 and 80 decibles
a researcher records the sound (in decibles) during a series of lessons taught by a substitute teacher at a local elementary school. which of the following is an appropriate conclusion? 80 +- 6
which of the following is the best explanation for why the standard deviation is almost always reported with the mean
the SD measures the spread if scores frim the mean, so it is important to know both the mean and the standard deviation
the degree of freedom for the sample variance
are equal to the sample size minus 1
what terms refer to each of the following measures, mean median and mode
average, middle, most
short answer: a researcher measures the following heights of CEO selected at random, which measure of central tendency is most appropriate ti use for describing these data? why?
median, because it is skewed
sketch a graph that shows a negative correlation between scores on a computer use and exercise
proper labels, and drawing negative scatter plot
when is the weighted mean equal to the arithmetic mean for combing the mean for two or more samples
when the sample sizes are equal
how many modes does a unimodel dis. have
1
a characteristic that describes a population for the population is called
parameter
A researcher has participants choose between three advertisements. She finds that 54 prefer Ad A, 86 prefer Ad B, and 60 prefer Ad C. The probability or proportion of participants preferring Ad B is
4.3
By definition, the probability of an outcome or event is
all of the above
Which of the following is NOT a characteristic of probability?
prob. is most useful for describing fixed events
Two outcomes are said to be mutually exclusive when
the prob. of the two outcomes occurring together is equal to zero (p=0)
In a game, the probability of winning money is p = .16, the probability of losing money is p = .54, and the probability of breaking even is p = .30. What is the probability of winning or losing money in this game?
.70
Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities?
multiplicative rule
A researcher reports that the probability of a college student living on campus is p = .38. If a small local college has 2,000 students enrolled, then what is the standard deviation of college students living on campus? Hint: This is a binomial probability distribution.
21.7
A researcher determines that the probability of missing class among students at a local school is p = .16. Assuming that the school has 300 students enrolled, how many students can we expect to miss class on a given day? Hint: This is a binomial probability distribution.
48 students
Each of the following is an example of a binomial distribution, except
the time it takes to complete the driving test
A researcher determines the probability that a research study will reveal something new is p = .80. What is the probability that the study will reveal something new or not reveal something new?
1.00
If the standard deviation of a probability distribution is 9, then the variance is
81
When the probability of one outcome changes depending on the occurrence of a second outcome, these outcomes are referred to as
conditional
The probability of a college student being employed is p = .35. The probability of a student being employed and dropping out of college is p = .20. Hence, the probability of a student dropping out of college, given that he or she is employed, is
p=.57
Which of the following allows researchers to use the standard normal distribution to estimate the probability of selecting sample means?
the central limit therom
Another name for a binomial variable is a
dichotomus variable
The normal distribution has all of the following characteristics, except
the total area under the curve is greater than 1.0
What is the implication for the tails of a normal distribution being asymptotic?
the extreme scores are possible in a normal distribution
Bayes' theorem is often applied to a variety of ________ probability situations, including those related to statistical inference.
conditional
The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at most five errors.
.71
The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making more than five errors
.29
The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at least three errors.
.57
The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at most two errors.
.43
The normal distribution is symmetrical, which means that
scores above the mean are distributed theame as scores below the mean
The standard normal distribution is normally distributed with a mean of ____ and a variance of ____.
0;1
The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a
z score
What is the z score for scores in the bottom 5%?
-1.645
State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the left of z = 0.80, or the area to the right of z = -0.80.
the two areas are the same
Which proportion is largest in a z distribution?
the proportion of area above the mean
Scores far from the mean are located in the ________ of a normal distribution.
tails
A normal distribution has a mean equal to 53. What is the standard deviation of this normal distribution if 2.5% of the proportion under the curve lies to the right of x = 66.72? (Round your answer to two decimal places)
7.00
How is the standard error of the mean typically reported in a graph?
using error bars
Each of the following statements are true, except that
the larger the sample size, the larger the standard error
Regardless of the shape of the distribution in the population, the sampling distribution of sample variances approximates a
positively skewed distribution
A researcher selects a sample of 16 participants from a population with a variance of 4. What is the standard error of the mean?
less than 1
Suppose that a researcher selects a sample of participants from a population. If the shape of the distribution in this population is positively skewed, then what is the shape of the sampling distribution of sample means?
approx. normal distributed
A researcher selects two samples of 64 participants each. In the first sample the population mean was 10 and the variance was 16. In this second sample, the population mean was 25 and the variance was 9. Which sample will be associated with a larger standard error of the mean?
sample 1
For the experimental sampling strategy,
sampling is without replacement
What values are distributed along the x-axis for a sampling distribution of the sample mean?
samples means
40. What values are distributed along the x-axis for a sampling distribution of the sample variance?
A) scores
B) sample means
C) sample variances
D) both B and C
C
41. A researcher selects a sample of size 4 from a population of size 6. How many possible samples of this size can be selected using experimental sampling?
A) 15
B) 30
C) 1,296
D) 4,096
A
42. The mean of the sampling distribution of sample means is
A) equal to the population mean
B) equal to the population variance
C) both A and B
D) none of the above
A
A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20. About 68% of the sample means in this sampling distribution should be between a sample mean of
A) 34 and 40
B) 34 and 38
C) 38 and 44
D) 36 and 40
D
44. (EXTRA CREDIT!!!) Increasing the number of observations or samples in a study will decrease the standard error (standard error of the mean). This is known as
A) Bob (not the right answer)
B) the law of diminishing returns
C) the theoretical law of estimtates
D) the law of large numbers
D
45. (EXTRA CREDIT!!!) How many possible samples of size 2 can be selected from a population of 5 using theoretical sampling?
A) 5
B) 10
C) 25
D) 32
C
47. (2pts) Why doesn't the z-table tell you probabilities for negative z-scores?
They are the same probabilities as for positive z-scores. That is, the normal distribution is symmetrical. E.g., The probability of getting a z-score above 2.5 is the same as that for getting a z-score below -2.5.
48. (4 pts) Given two outcomes, A and B, state their relationship as a conditional probability using a "given" statement. (Hint: Be sure to state BOTH possible conditional probabilities).
2pts): the probability of A, given that B occurs, (2pts) the probability of B, given that A occurs
(4 pts) Assume number of days absent is normally distributed. If a sample mean is 8 and SD is 2, what's the z-score for a person with 2 days absent?
-3
A method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample, is called
A) hypothesis testing
B) guessing
C) level of significance
D) random sampling
A
A professor gives an exam in which the mean score is 78 points. She gives another exam to test whether or not scores change. In this example, the null hypothesis is
A) M = 78
B) u = 78
C) u broken = 78
D) M broken = 78
b
3. Which of the following statements regarding the null hypothesis is true?
A) The null hypothesis is the only hypothesis stated in hypothesis testing.
B) The null hypothesis always makes statements about a population parameter.
C) A decision in hypothesis testing is made about the alternative hypothesis, not the null hypothesis.
D) all of the above
b
What is the typical level of significance for a hypothesis test in behavioral research?
A) .50
B) .001
C) .05
D) .10
c
The one-sample z test is a hypothesis test used to test hypotheses
A) concerning at least one population
B) concerning the variance in a population
C) concerning a single population with a known variance
D) all of the above
C
A researcher obtains z = 1.45 for a one-sample z test. What is the decision for this test at a .05 level of significance?
A) It depends on whether the test is one-tailed or two-tailed.
B) to reject the null hypothesis
C) to retain the null hypothesis
D) There is not enough information to make a decision.
C
7. ________ allows researchers to describe (1) how far mean scores have shifted in the population, or (2) the percentage of variance that can be explained by a given variable.
A) Power
B) Effect size
C) Probability
D) Significance
B
8. A researcher reports that the size of an effect in some population is d = 0.88. Which of the following is an appropriate interpretation for d?
A) Mean scores were significant by 0.88 points in the population.
B) The effect observed in the population was significant.
C) Mean scores shifted 0.88 standard deviations in the population.
D) Mean scores were significant by 0.88 points in the sample.
C
9. When reporting the results of a one-sample z test using APA format, the ________ does not need to be reported.
A) critical values
B) effect size
C) Test statistic
D) p value
A
Is a one-sample z test reported differently for one-tailed and two-tailed tests?
A) It depends on whether the results were significant.
B) It can be reported differently when the effect size is large.
C) No, the same values are reported.
D) Yes, only significant results for a two-tailed test are reported.
C
11. The ________ is an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis.
A) degrees of freedom
B) t distribution
C) t statistic
D) standard error
C
The t distribution is similar to the z distribution except
A) it is associated with scores being more likely in the tails of the distribution
B) it is associated with greater variability
C) it is characterized by "thicker" tails compared with the z distribution
D) all of the above
D
The estimated standard error in the t statistic uses the ________ to estimate the ________ when the population variance is unknown.
A) standard error; sample variance
B) sample variance; population variance
C) degrees of freedom; sample size
D) population variance; sample variance
B
State the critical value(s) for a t test using a two-tailed test at a .05 level of significance: t(20).
A) ±2.093
B) ±0.687
C) ±1.725
D) ±2.086
D
15. A researcher selects a sample of 32 participants who are assigned to participate in a study with one group. What are the degrees of freedom for this test?
A) 30
B) 31
C) 32
D) There is not enough information to answer this question.
B
A researcher conducts two t tests. Test 1 is a one-tailed test with a smaller sample size at a .05 level of significance. Test 2 is a one-tailed test with a larger sample size at a .05 level of significance. What do you know about the critical values for each test?
A) Test 2 is associated with smaller critical values.
B) Each test is associated with the same critical values.
C) Test 1 is associated with smaller critical values.
D) It depends; there is not enough information to answer this question.
A
17. Which of the following is an assumption for computing any type of independent sample t test?
A) Data were obtained from a sample that was selected using a random sampling procedure.
B) The probabilities of each measured outcome in a study are independent.
C) Data in the population being sampled are normally distributed.
D) all of the above
D
Computing a one-sample t test is appropriate when
A) participants are observed one time
B) participants are assigned to only one group
C) the population variance is unknown
D) all of the above
D
The mean crying time of infants during naptime at a local preschool is 12 minutes (that's the population mean). The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8±4.6 (M±SD) minutes. Calculate t.
A) 0.92
B) 4.35
C) -0.92
D) -4.35
D
Which of the following is an assumption for the two-independent sample t test, but not the one-sample t test?
A) Equal variances
B) Independence
C) Normality
D) Random sampling
A
21. To compute a two-independent sample t test, a researcher has to know many values. Which of the following is NOT a value that the researcher must know to compute this test?
A) the sample mean for both samples
B) the pooled sample variance
C) the pooled population variance
D) the sample size for both samples
C
A researcher runs an independent groups design and reports that the mean difference in response time to an auditory versus a visual cue is 0.83 seconds, with a pooled sample variance equal to 2.45. What is the effect size for this test using estimated Cohen's d?
A) d = 0.53
B) d = 1.00
C) d = 0.34
D) d = 0.83
A
Which measure of effect size is most commonly reported with a t test?
A) omega-squared
B) t statistic
C) Cohen's d
D) eta-squared
C
A researcher has participants rate the likability of a sexually promiscuous person described in a vignette as being male (n = 20) or female (n = 12). The mean likability ratings in each group were 4.0. If the null hypothesis is that there is no difference in likability ratings, then do likability ratings differ at a .05 level of significance?
A) No, this result is not significant, t(30) = 0.
B) No, this result is not significant, t(30) = 1.00.
C) Yes, this result is significant, p < .05.
D) There is not enough information to answer this question, because the variance in each sample is not given.
A
A type of related samples design in which participants are observed more than once is called a
A) repeated measures design
B) matched pairs design
C) matched samples design
D) both B and C
A
One difference between a repeated measures design and a matched samples design is that
A) only one design eliminates between-persons variability
B) only one design is a type of related sample design
C) only one design increases the power to observe an effect
D) only one design involves observing the same participants in each group
D
The test statistic for a related samples t test makes tests concerning a single sample of
A) participant scores
B) original data
C) difference scores
D) raw scores
C
For the related samples t test, assuming that all other values remain constant, then as samples size increases,
A) the estimate for standard error decreases
B) the value of the test statistic increases
C) the power to detect an effect increases
D) all of the above
D
29. A researcher records the time it takes (in seconds) for participants to respond (by pressing a key) to a familiar versus an unfamiliar word flashed onto a computer screen. In this study, the difference in response time for each participant is compared. The type of design described here is called a
repeated measures design
A researcher selects a sample of 36 dog owners and measures their responsiveness to two types of pictures: one depicting the humane treatment of dogs and one depicting the inhumane treatment of dogs. The researcher finds that responsiveness significantly differed, t = 3.243. Use eta-squared to compute the proportion of variance for this result.
A) = 0.25
B) = 0.21
C) = 0.23
D) There is not enough information to answer this question.
C
A researcher sampled 16 couples and measured the mean difference in their marital satisfaction. Each couple was paired and the differences in their ratings (on a 7-point scale) were taken. If the mean difference in satisfaction ratings for this sample was 1.8±2.0 ( ), then what is the decision at a .05 level of significance?
A) Satisfaction ratings significantly differ, t(14) = 3.60.
B) Satisfaction ratings significantly differ, t(15) = 3.60.
C) Satisfaction ratings do not significantly differ, t(15) = 0.90.
D) Satisfaction ratings do not significantly differ, t(14) = 0.90.
B
32. Compared to the two-independent sample t test, the related samples design decreases
A) standard error
B) significance
C) effect size
D) power
A
33. Using APA format, which value is typically given in parentheses when reporting the results for a t test?
A) The estimate for standard error.
B) The level of significance.
C) The degrees of freedom.
D) The value of the test statistic.
C
34. Using a between-subjects ANOVA design,
A) n participants are observed k times
B) the same participants are observed in each group
C) participants are each observed one time
D) data are not analyzed between groups
A
For an analysis of variance, the term "one-way" refers to
A) the number of ways that the data can be analyzed
B) the direction that traffic should follow on a road
C) the number of statistical tests in the design
D) the number of factors in the design
D
A researcher compares differences in positivity between participants in a low-, middle-, or upper-middle-class family. If she observes 15 participants in each group, then what are the degrees of freedom for the one-way between-subjects ANOVA?
A) (3, 12)
B) (2, 12)
C) (3, 43)
D) (2, 42)
D
Computing a one-way between-subjects ANOVA is appropriate when
A) the same participants are observed in each of two or more groups for one factor
B) the levels of one or more factors are manipulated
C) different participants are observed one time in each of two or more groups for one factor
D) all of the above
C
Homogeneity of variance is an assumption for the one-way between-subjects ANOVA. What does this assumption mean?
A) that one observation has no effect on the likelihood of another observation
B) that the population being sampled from is normally distributed
C) that participants are randomly selected to participate in a sample
D) that the variance is equal in each population from which samples are selected
D
39. Post hoc tests are computed
A) to determine if groups means differ, even for tests in which the decision is to retain the null hypothesis.
B) Following a significant ANOVA test to make pairwise comparisons.
C) Prior to conducting a hypothesis test.
D) To determine which set of degrees of freedom can be attributed to the variability between-groups.
B
The following is a summary of a one-way between-subjects ANOVA: F(2, 37) = 3.42, p < .05, = .12. How many participants were observed in this study?
A) 39
B) 12
C) 37
D) 40
D
41. (EXTRA CREDIT) A researcher assigned participants (n = 8 per group) to read vignettes describing a person engaging in either a helpful, hurtful, or neutral act. Different participants were assigned to each group and asked to rate how positively they viewed the person described in the vignette. What is the critical value for the one-way between-subjects ANOVA at a .05 level of significance?
A) 4.32
B) 3.47
C) 3.07
D) 3.44
B
(EXTRA CREDIT) Using a two-way between-subjects ANOVA with Factor A (Gender: male, female) and Factor B (Type of employment: blue collar, white collar), a researcher found that salary for men and women significantly varied across the levels of the second factor (type of employment). That is, the effect of gender depended on type of employment. In this study, the researcher found a significant
A) post hoc test
B) main effect of Factor A
C) main effect of Factor B
D) interaction
D
Give the definition of "power" in statistics usage.
The Likelihood of rejecting a false null hypothesis
. (4 pts) The text below (at the bottom of the page) was taken from an APA style results section from a manuscript. However, one of the numbers is clearly wrong (must have been a typo!). Assume that all of the wording is correct and that all of the other parts are correct. Assuming that's true, answer these two questions:
a. Which number is wrong?
b. How should it be changed? (I.e., what's wrong with it, exactly?)
"The one-way ANOVA reached significance, F(2,27) = 3.52, p = .45 ( = 0.14). Post hoc tests showed that the time employees said they would stay was significantly greater for those who rated the workplace as low-stress compared to those rated it high-stress (Tukey HSD, p < .05). Otherwise no significant differences were found (p > .05).
a. .45
b. it should be less than .05
A professor finds that the average SAT score among all students attending his college (i.e., in that population) is 1150±150 ( ). He polls his class of 25 students and finds that the average SAT score is 1200. Compute a one-sample z test. Also, state whether he would reject the null hypothesis with a two-tailed test with a .05 level of significance. (Be sure to show your work).
z= 1.67, No: do not reject the null hypothesis
(2 points). One type of ANOVA design is a(n)_____________________________ design, which is defined as the situation when at least one independent variable is between groups and at least one independent variable is within groups.
mixed
Retaining a false null hypothesis is a Type____________________error.
2
Circle the correct answer at the end of this statement: As a researcher, you want your effect size to be small/large.
large
In lecture, more complex ANOVA designs were described. For example, in a three-way ANOVA, how many factors (independent variables) are tested?
3
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