61 terms

# chi square

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The actual counts in the cells of a contingency table are referred to as the expected cell frequencies.
False
When we carry out a chi-square test for independence, the null hypothesis states that the tow relevant classifications.
D. The alternative hypothesis states that the two classifications are statistically independent
NOT If ri is the row total for row i and cj is the column total for column j, then the estimated expected cell frequency corresponding to row i and column j equals ricj/n.
The chi-square test is valid if all of the estimated expected cell frequencies are at least 5.
The chi-square statistic is based on (r-i) (c-i) degrees of freedom where r and c denote the number of rows and columns respectively in the contingency table.
None of the above.
Which of the following statements about the chi-square test of independence is false?
The alternative hypothesis states that the two classifications are statistically independent.
NOTIf ri is the row total for row i and cj is the column total for column j, then the estimated expected cell frequency corresponding to row i and column j equals ricj/n.
The chi-square test is valid if all of the estimated expected cell frequencies are at least 5.
The chi-square statistic is based on (r-i) (c-i) degrees of freedom where r and c denote the number of rows and columns respectively in the contingency table.
None of the above.
In a contingency table, when all the expected frequencies equal the observed frequencies the calculated x2 statistic equals zero.
True
When using chi-square goodness of fit test with multinomial probabilities, the rejection of the null hypothesis indicates that at least one of the multinomial probabilities is not equal to the value stated in the null hypothesis.
True
A fastener manufacturing company uses chi-square goodness of fit test to determine if the population of all lengths of 1/4 inch bolts it manufactures is distributed according to a normal distribution. If we reject the null hypothesis, it is reasonable to assume that the population distribution is at least approximately normally distributed.
False
When using the chi-square goodness of fit test, if the value of the chi-square statistic is large enough, we reject the null hypothesis
True
In performing a chi-square test of independence, as the difference between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable
Correct: increases
NOT decreases
may decrease of increase depending on the number of rows and columns.
remains the same.
A chi-square goodness of fit test is considered to be valid if each of the expected cell frequencies is ___________________.
E. at least 5.
NOT
greater than zero.
less than 5.
between 0 and 5.
at most 1
The x2 statistic from a contingency table with 6 rows and five columns will have _____ degrees of freedom
correct: 20
NOT 30 24 5 25
The chi-square goodness of fit test is _________ a one-tailed test with the rejection point in the right tail.
Yes always NOT sometimes or never
The x2 statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5000 observations and is divided into 6 categories (intervals). The degrees of freedom for the chi-square statistic is:
correct 3
NOT 4999 6 5 4
The process of using sample statistics to draw conclusions about true population parameters is called:
Statistical inference
The process of using sample statistics to draw conclusions about true population parameters is called:
Statistical inference
The classification of student class designation (freshman, sophomore, junior, senior) is an example of:
Categorical random variable
To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot each 30 minutes of a 24-hour period with the goal of determining when patrols of the lot would serve the most students. If X is the number of students in the lot each period of time, then X is an example of:
a discrete random variable
The personnel director at a large company studied the eating habits of the company's employees. The director noted whether employees brought their own lunches to work, ate at the company cafeteria, or went out to lunch. The goal of the study was to improve the food service at the company cafeteria. This type of data collection would best be considered as:
an observational study
A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether or not they studied for the exam before the midterm, and whether they did well or poorly on the midterm. The following table contains the result.

Did Well in Midterm Did Poorly in Midterm
Studied for the exam 80 20
Did not study for the exam 30 70

Referring to the above table, of those who did not study for the exam, _______ percent of them did well on the midterm.
30
An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. A representative from a local insurance agency selected a random sample of insured drivers and recorded, X, the number of claims each made in the last 3 years, with the following results.
X f
50
Which measure of central tendency can be used for both numerical and categorical variables?
mode
Which of teh following is NOT a measure of central tendency?
interquartile range
A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Disappointing
20%
The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is:
0.733
Thirty-six of the staff of 80 teachers at a local school are certified in CPR. In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified?
81
If n=10 and p=0.70, then the mean of the binomial distribution is:
7.00
A professor receives, on average, 24.7 e-mails from her students per 24 hour period on the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, what type of probability distribution should be used?
Poisson distribution
For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. Therefore the value of Z is:
1.16
FoFor some positive value of X, the probability that a standard normal variable is between 0 and +1.5X is equal to 0.4332. Therefore the value of X is:
1.00
If a particular batch of data is approximately normally distributed, we would find that approximately
2 of every 3 observations would fall between 1 standard deviation above and below the mean.
4 of every 5 observations would fall between 1.28 standard deviation above and below the mean.
19 of every 20 observations would fall between 2 standard deviation above and below the mean.
ALL OF THE ABOVE
A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately normally distributed with a mean of 68 years of age and a standard deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age 75?
0.0228
You work at Smuckers in Orrville, Ohio and are in charge of the grape jelly production line. The weight of jars of grape jelly and the number of jars at each weight for the last month (4 weeks) are as follows:
Weight # Jars
8.0 oz. 300
8.5 oz. 287
8.9 oz. 128
9.0 oz. 67
You work at Smuckers in Orrville, Ohio and are in charge of the grape jelly production line. The weight of jars of grape jelly and the number of jars at each weight for the last month (4 weeks) are as follows:
0.1366
There are 5 starting players on the Bulldog basketball team. Each player wanted to improve her shooting percentage, especially Hannah. The number of baskets Hannah made in the last 10 games are listed below:

12,13,21,18,19,8,4,22,12,27
Calculate the mean, median, mode, variance and standard deviation and range and list them in that order.
15.6, 15.5, 12, 49.16, 7.01, 23
The width of a confidence interval estimate for a proportion will be:
narrower for 90% confidence than for 95% confidence
If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample s=0.05, the critical value of t will be:
2.7969
A confidence interval was used to estimate the proportion of statistics students who are females. A random sample of 72 students generated a 90% confidence interval of 0.438 to 0.642. Therefore, it is reasonable to assume that the population of female students should be above 50%.
False
Suppose a 95% confidence interval turns out to be 1,000 to 2,100. If the researcher wishes to reduce the width of the interval. One way he can do that is to increase the sample size
True
A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the store. 85 accounts were randomly selected. The 95% confidence interval was \$56.89 t0 \$145.78. Therefore, the store manager can be 95% confident that
most of his customers are spending more than \$50
If the calculated Z-score falls in the rejection region (in the tail of the bell curve), then the null hypothesis is:
rejected
A Type II error is committed when we reject a null hypothesis that is true.
False
How many Kleenex should a Kimiberly Clark Corp. package of tissues contain? Researchers determined that, on average, a person uses 60 tissues during a cold, and the population standard deviation is 22. Suppose a random sample of 100 Kleenex users yielded a mean of 52. Test the following hypothesis at the 5% significance level.
Critical Value = 1.96; Calculated Z = 3.64; Reject the null hypothesis
Given your conclusion in question #8, you should recommend that Kimberly Clark Corp. put more than 60 tissues in each box.
False
In a sample of 265 subjects, the average score on an examination was 63.8. Historically, the population standard deviation has been σ = 3.08. What is the 95% confidence interval estimate for the µ?
[63.43 to 64.17]
When testing for independence in a contingency table with 3 rows and 4 columns, there are ______ degrees of freedom.
6
If we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2, the appropriate tests to use are the Z test and the chi-square test
True
A manufacturing company produces bike frames and makes 1200 per year. These bike frames can be produced using three different processes. Each process has a unique cost associated with it. The CEO wants to know if the manufacturing processes are related to the overall cost of bike frame production. The following contingency table gives the number of bike frames produced with each process and cost level. At a significance level of .05, perform the chi-square test of independence to determine if production process is related to production cost.
5.99 CRITICAL VALUE
12.56 CHI SQUARE VALUE
5. Question : In the past, of all the students enrolled in "Basic Business Statistics" 10% earned A's, 20% earned B's, 30% earned C's, 20% earned D's and the remaining 20% either failed or withdrew from the course.

Dr Johnson is a new professor teaching "Basic Business Statistics" for the first time this semester. At the conclusion of the semester, in Dr. Johnson's class of 60 students, there were 10 A's, 20 B's, 20 C's, 5 D's and 5 W's or F's.

Assume that Dr. Johnson's class constitutes a random sample. Dr Johnson wants to know if there is sufficient evidence to conclude that the grade distribution of his class is different than the historical grade distribution.

Use a = .05, and determine if the grade distribution for Dr. Johnson's class is different than the historical grade distribution.
Reject the null hypothesis at the 5% level of significance because 16.4 > 9.48 Therefore there is a difference between the historical grade distribution and Dr. Johnson's
In a contingency table, when all the expected frequencies equal the observed frequencies the calculated Chi-square statistic equals zero.
True
The actual counts in the cells of a contingency table are referred to as the expected cell frequencies
False
In general, the degrees of freedom in a contingency table are equal to:
(rows -1)(columns-1)
The chi-square goodness of fit is always a one-tailed test with the rejection region in the right tail.
True
When conducting the chi-square goodness of fit test for your Integrated Research Project, you will be using "Agree, Disagree and No opinion" for your survey responses. Therefore the degrees of freedom used to obtain the critical value is 2.
False
The Dalton Baseball Team is trying to analyze the number of hits thier team got last season in order to train in the off season and improve their record for next season. The number of hits each of the 15 players received are as follows:
Baseball Player # Hits
1 34
2 21
3 14
4 13
5 15
6 16
7 19
8 21
9 9
10 11
11 18
12 21
13 14
14 21
15 16
18, 21, 15

21, 16.53, 23

X 17.53, 16, 21
The weather is bad for the Northern Ohio area and storms are being forecasted. If the probability of a thunderstorm hitting Canton, Ohio, is 67%, and the probability of hail is 34%, and the probability of both a thunderstorm and hail hitting is 28%, what then is the probability of either a thunderstorm or hail hitting the Canton, Ohio are today?
73%
The t distribution approaches the _______________ as the sample size ___________.
Z, increases
When the sample size and sample standard deviation remain the same, a 99% confidence interval for a population mean, µ will be _________________ the 95% confidence interval for µ
Wider than
When the population is normally distributed, population standard deviation s is unknown, and the sample size is n = 15; the confidence interval for the population mean µ is based on:
The t distribution
In a manufacturing process a random sample of 36 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99% confidence interval for the true mean length of the bolt?
2.865 to 3.136
The chi-square goodness of fit test for multinomial probabilities with 5 categories has _____ degrees of freedom
4
A U.S. based internet company offers an on-line proficiency course in basic accounting. Completion of this online course satisfies the "Fundamentals of Accounting" course requirement in many MBA programs. In the first semester 315 students have enrolled in the course. The marketing research manager divided the country into seven regions of approximately equal populations. The course enrollment values in each of the seven regions are given below. The management wants to know if there is equal interest in the course across all regions. 45,60,30,40,50,55,35,
15.56
You have diligently collected your surveys and crunched all of the numbers for your primary research on your IRP. One of the questions you asked was as folows:
The Orrville Public Library would see an increase in number of customers if they extended their evening hours to stay open until 11:00 pm on weekend nights.
You had 57 surveys collected from library adminstrators and staff, with 39 Agree and 10 disagree. What is the calculated Chi-Square value for this test?
17.16
You have diligently collected your surveys and crunched all of the numbers for your primary research on your IRP. One of the questions you asked was as folows:
The Orrville Public Library would see an increase in number of customers if they extended their evening hours to stay open until 11:00 pm on weekend nights.
You had 57 surveys collected from library adminstrators and staff, with 39 Agree and 10 disagree. Based on the calculated Chi-square value from above, what is the critical value you will compare that to and is this data now proven to be significant?
The critical value is 3.84, an yes it is significant