Statistics Final Exam (11,12,13)

If we are testing for the equality of 3 population means, we should use the _____.

*test statistic χ2* test statistic t test statistic F test statistic z

Exhibit 11-10 n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 Refer to Exhibit 11-10. The p-value is between _____

.05 and .1 .2 and .3 *.1 and .2* .025 and .05

Exhibit 13-5 Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 180 3 Within treatments (Error) Total 480 18 ​ Refer to Exhibit 13-5. The mean square between treatments (MSTR) is _____.

20 15 *60* 300

A random sample of 31 charge sales showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is _____.

39.96 to 66.83 *41.39 to 63.68* 1,596.45 to 4,466.73 1,715.10 to 4,055.68

Exhibit 11-4 n = 30 H0: σ2 = 500 s2 = 625 Ha: σ2 ≠ 500 Refer to Exhibit 11-4. The test statistic for this problem equals _____.

37.5 23.2 *36.25* 24

The χ2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 25 is _____.

37.6525 33.1963 *36.4151* 39.3641

Which of the following has an F distribution?

(n-1)s ------- σ

The independent variable of interest in an ANOVA procedure is called _____.

a treatment either a partition or a treatment a partition *a factor*

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

factor block design random factor design None of the answers is correct. *completely randomized design*

A random sample of 31 charge sales showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is _____.

1,715.10 to 4,055.68 39.96 to 66.83 1,596.45 to 4,466.73 *41.39 to 63.68*

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is _____.

1.96 *2.25* 3.74 2.37

Exhibit 11-8 n = 23 H0: σ2 ≥ 66 s2 = 60 Ha: σ2 < 66 Refer to Exhibit 11-8. The test statistic has a value of _____.

24.00 24.20 *20.00* 20.91

The symbol used for the variance of the sample is _____.

σ2 σ *s2* s

Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 ​ Refer to Exhibit 13-2. The null hypothesis is to be tested at the 5% level of significance. The critical value from the table is _____.

*2.87* 2.71 5.19 5.8

Exhibit 12-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year's student body showed the following number of students in each class. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year. Refer to Exhibit 12-2. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals _____.

*7.815* 1.645 1.96 2.75

x^2 .975= 8.9066 indicates that _____.

*97.5% of the chi-square values are greater than 8.9066* 2.5% of the chi-square values are greater than 8.9066 5% of the chi-square values are more than 8.9066 from the mean 97.5% of the chi-square values are less than 8.9066

The mean square is the sum of squares divided by _____.

*its corresponding degrees of freedom* the total number of observations None of the answers is correct. its corresponding degrees of freedom minus1

A sample of n observations is taken from a population. When performing statistical inference about a population variance, the appropriate χ2 distribution has _____.

*n - 1 degrees of freedom* n - 3 degrees of freedom n degrees of freedom n - 2 degrees of freedom

Exhibit 11-2 We are interested in determining whether the variances of the sales at two music stores (A and B) are equal. A sample of 25 days of sales at store A has a sample standard deviation of 30, while a sample of 16 days of sales from store B has a sample standard deviation of 20. Refer to Exhibit 11-2. At 95% confidence, the null hypothesis _____.

*should not be rejected* None of the answers is correct. should be rejected should be revised

Exhibit 11-6 Sample A Sample B s2 32 38 n 24 16 We want to test the hypothesis that the population variances are equal. Refer to Exhibit 11-6. The null hypothesis _____.

*should not be rejected* None of the answers is correct. should be revised should be rejected

A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounce. A 95% confidence interval estimate of the variance for the population is _____.

.2313 to .8533 .2224 to .7924 *.0925 to .3413* .0889 to .3169

Exhibit 12-5 The table below gives beverage preferences for random samples of teens and adults. Beverage Teens Adults Total ---------------------------------------------------- Coffee 50 200 250 Tea 100 150 250 Soft drink 200 200 400 Other 50 50 100 -------------------------------------- 400 600 1,000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 12-5. If age and drink preference is independent then the expected number of adults who prefer coffee would be _____.

.25 .33 *200* 150

Exhibit 13-1 SSTR = 6,750 H0: μ1 = μ2 = μ3 = μ4 SSE = 8,000 Ha: At least one mean is different nT = 20 ​ ​ Refer to Exhibit 13-1. The test statistic to test the null hypothesis equals _____.

.84 4.22 *4.5* .22

Exhibit 12-6 The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. Political Party Support Democrats 100 Republicans 120 Independents 80 We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. Refer to Exhibit 12-6. The calculated value for the test statistic equals_____.

0 *8* 300 4

Exhibit 13-7 The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total ​ Refer to Exhibit 13-7. The number of degrees of freedom corresponding to between treatments is _____.

12 4 *2* 3

Exhibit 11-5 n = 14 H0: σ2 ≤ 410 s = 20 Ha: σ2 > 410 Refer to Exhibit 11-5. The test statistic for this problem equals _____.

13.66 *12.68* 13.33 .63

Exhibit 11-9 n = 14 s = 20 H0: σ2 ≤ 500 Ha: σ2 ≥ 500 Refer to Exhibit 11-9. The test statistic for this problem equals _____.

13.66 13.33 *12.68* .63

Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 ​ Refer to Exhibit 13-2. The sum of squares due to error equals ____

14.4 2,073.6 6,000 *5,760*

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments. The following information is provided. ​ SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. The sum of squares within treatments (SSE) is _____.

200 1,000 1,600 *600*

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is _____.

3.63 2.58 *2.48* 2.96

The critical F value with 8 numerator and 29 denominator degrees of freedom at α = .01 is _____.

3.64 3.33 *3.20* 2.28

Exhibit 13-7 The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total ​ Refer to Exhibit 13-7. The mean square between treatments (MSTR) is _____.

36 *32* 16 8

An ANOVA procedure is used for data that were obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are _____.

4 and 17 3 and 19 3 and 20 *3 and 16*

An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____.

4 and 20 4 and 99 5 and 20 *4 and 95*

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are _____.

6 numerator and 20 denominator degrees of freedom 5 numerator and 20 denominator degrees of freedom 6 numerator and 20 denominator degrees of freedom *5 numerator and 114 denominator degrees of freedom*

Exhibit 13-7 The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total ​ Refer to Exhibit 13-7. The computed test statistic is _____.

8 .667 32 *4*

In an analysis of variance problem, if SST = 120 and SSTR = 80, then SSE is _____.

80 120 *40* 200

In Excel, which of the following functions is used to construct a confidence interval for a population variance?

F-Test CHISQ.DIST *CHI.INV* None of the answers is correct.

The bottler of a certain soft drink claims its equipment to be accurate and that the variance of all filled bottles is .05 or less. The null hypothesis in a test to confirm the claim would be written as _____.

H0: σ2 > .05 H0: σ2 < .05 H0: σ2 ≥ .05 *H0: σ2 ≤ .05*

Which of the following is NOT a required assumption for the analysis of variance?

The random variable of interest for each population has a normal probability distribution. The variance associated with the random variable must be the same for each population. At least two populations are under consideration. *Populations have equal means.*

A goodness of fit test is always conducted as a(n) _____.

middle test None of the answers is correct. *upper-tail test* lower-tail test

Exhibit 12-6 The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. Political Party Support Democrats 100 Republicans 120 Independents 80 We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. The test for goodness of fit, test of independence, and test of multiple proportions are designed for use with _____.

ordinal data quantitative data bivariate data *categorical data*

In an analysis of variance, one estimate of is based upon the differences between the treatment means and the _____.

overall sample mean *populations have equal means* means of each sample sum of observations

A term that means the same as the term "variable" in an ANOVA procedure is _____.

replication *factor* treatment variance within

To avoid the problem of having access to tables of the F distribution with values for the lower tail when a one-tailed test is required, let the _____ variance be the numerator of the test statistic.

sample variance from the population with the larger hypothesized *sample variance from the population with the smaller hypothesized* larger sample smaller sample

The required condition for using an ANOVA procedure on data from several populations is that the _____.

sampled populations are all uniform sampled populations have equal means selected samples are dependent on each other *sampled populations have equal variances*

Exhibit 11-5 n = 14 H0: σ2 ≤ 410 s = 20 Ha: σ2 > 410 Refer to Exhibit 11-5. The null hypothesis _____.

should be rejected should be revised *should not be rejected* None of the answers is correct.

Exhibit 13-1 SSTR = 6,750 H0: μ1 = μ2 = μ3 = μ4 SSE = 8,000 Ha: At least one mean is different nT = 20 ​ ​ Refer to Exhibit 13-1. The null hypothesis _____.

should not be rejected was designed incorrectly None of the answers is correct. *should be rejected*

Exhibit 11-6 Sample A Sample B s2 32 38 n 24 16 We want to test the hypothesis that the population variances are equal. Refer to Exhibit 11-6. The test statistic for this problem equals _____.

.67 *1.19* 1.50 .84

Exhibit 11-2 We are interested in determining whether the variances of the sales at two music stores (A and B) are equal. A sample of 25 days of sales at store A has a sample standard deviation of 30, while a sample of 16 days of sales from store B has a sample standard deviation of 20. Refer to Exhibit 11-2. The test statistic is _____.

2.25 1.50 .67 *1.56*

Exhibit 11-6 Sample A Sample B s2 32 38 n 24 16 We want to test the hypothesis that the population variances are equal. Refer to Exhibit 11-6. The null hypothesis is to be tested at the 10% level of significance. The critical value from the table is _____.

2.29 *2.13* 2.24 2.11

The χ2 value for a one-tailed test (lower tail) when the level of significance is .1 and the sample size is 15 is _____.

21.064 *7.78453* 23.6848 6.57063

The producer of a certain medicine claims that its bottling equipment is very accurate and that the standard deviation of all its filled bottles is 0.1 ounce or less. A sample of 20 bottles showed a standard deviation of .11. The test statistic to test the claim is _____.

400 *22.99* 20 4.85

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is _____.

51.25 10 *50* 100

Which of the following rejection rules is proper?

Reject H0 if p-value ≥ Reject H0 if p-value ≥ Fα *Reject H0 if p-value < a* Reject H0 if p-value ≤ X^2a

In a goodness of fit test, Excel's CHISQ.DIST.RT function returns a _____.

chi-square critical value *p-value* confidence interval estimate chi-square test statistic

Which of the following has a χ2 distribution?

(n - 2)σ2/s2 (n - 1)s2/σ2 *(n - 1)σ2/s2* (n - 1)s/σ

A sample of 60 items from population 1 has a sample variance of 8, while a sample of 40 items from population 2 has a sample variance of 10. If we test whether the variances of the two populations are equal, the test statistic will have a value of _____.

*1.25* 1.5 .8 1.56

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether the proportions have changed, a random sample of 300 students from ABC University was selected. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 12-4. If the proportions are the same as they were in the past, the expected frequency for the Business College is _____.

*105* 90 .35 .3

A sample of 21 elements is selected to estimate a 90% confidence interval for the variance of the population. The χ2 value(s) to be used for this interval estimation is(are) _____.

*12.443 and 28.412* 12.443 10.851 and 31.410 -1.96 and 1.96

The degrees of freedom for a contingency table with 12 rows and 12 columns is _____.

*121* 144 12 120

The χ2 values (for interval estimation) for a sample size of 10 at 95% confidence are _____.

*2.70039 and 19.0228* 3.32511 and 16.9190 4.16816 and 14.6837 3.24697 and 20.4831

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments. The following information is provided. ​ SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. The number of degrees of freedom corresponding to between treatments is _____.

*4* 59 60 5

Exhibit 12-3 In order to determine whether a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Patients Cured Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether the medication was effective in curing the common cold. Refer to Exhibit 12-3. If the proportion of patients that are cured is independent of whether the patient received medication then the expected frequency of those who received medication and were cured is _____.

*48* 28 70 150

Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 ​ Refer to Exhibit 13-2. The mean square between treatments equals _____.

*518.4* 8,294.4 288 1,200

Exhibit 12-5 The table below gives beverage preferences for random samples of teens and adults. Beverage Teens Adults Total ---------------------------------------------------- Coffee 50 200 250 Tea 100 150 250 Soft drink 200 200 400 Other 50 50 100 -------------------------------------- 400 600 1,000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 12-5. With a .05 level of significance, the critical value for the test is _____.

*7.815* 14.067 15.507 1.645

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The null hypothesis is to be tested at the 1% level of significance. The critical value from the table is _____.

*8.02* 16.69 99.39 4.26

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The mean square between treatments (MSTR) equals _____.

1.872 34 5.86 *36*

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The mean square within treatments (MSE) equals _____.

1.872 36 *34* 5.86

Exhibit 12-1 Individuals in a random sample of 150 were asked whether they supported capital punishment. The following information was obtained. Do You Support # of Individuls Capital Punishment? Yes 40 No 60 No Opinion 50 We are interested in determining whether the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 12-1. If the opinions are uniformly distributed, the expected frequency for each group would be _____.

1/3 .333 *50* .50

Exhibit 12-6 The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. Political Party Support Democrats 100 Republicans 120 Independents 80 We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. Refer to Exhibit 12-6. The test statistic for goodness of fit has a chi-square distribution with k - 1 degrees of freedom provided that the expected frequencies for all categories are _____.

10 or more k or more *5 or more* 2k

Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounce. We are interested in testing to determine whether the variance of the population is significantly more than .003. Refer to Exhibit 11-3. At 95% confidence, the critical value(s) from the table is(are) _____.

14.6114 14.6114 and 37.6525 *37.6525* 13.1197 and 40.646

Exhibit 12-3 In order to determine whether a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Patients Cured Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether the medication was effective in curing the common cold. Refer to Exhibit 12-3. The number of degrees of freedom associated with this problem is _____.

149 4 3 *1*

Exhibit 13-7 The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total ​ Refer to Exhibit 13-7. The number of degrees of freedom corresponding to within treatments is _____.

15 3 2 *12*

Exhibit 12-1 Individuals in a random sample of 150 were asked whether they supported capital punishment. The following information was obtained. Do You Support # of Individuls Capital Punishment? Yes 40 No 60 No Opinion 50 We are interested in determining whether the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 12-1. The number of degrees of freedom associated with this problem is _____.

150 3 *2* 149

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The test statistic to test the null hypothesis equals _____.

19.231 .944 3.13 *1.059*

In a hypothesis test about two population variances, the test statistic F is computed as _____.

2 S 1 ------- 2 S 2

Exhibit 13-5 Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 180 3 Within treatments (Error) Total 480 18 ​ Refer to Exhibit 13-5. The mean square within treatments (MSE) is _____.

300 *20* 15 60

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments. The following information is provided. ​ SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. If at a 5% level of significance we want to determine whether or not the means of the five populations are equal, the critical value of F is _____.

39.48 4.98 19.48 *2.53*

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments. The following information is provided. ​ SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. The number of degrees of freedom corresponding to within treatments is _____.

4 *60* 59 5

Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 ​ Refer to Exhibit 13-2. The null hypothesis is to be tested at the 5% level of significance. The critical value from the table is _____.

5.8 *2.87* 5.19 2.71

Exhibit 12-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year's student body showed the following number of students in each class. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year. Refer to Exhibit 12-2. The calculated value for the test statistic equals _____.

6.6615 *1.6615* .5444 300

Exhibit 12-1 Individuals in a random sample of 150 were asked whether they supported capital punishment. The following information was obtained. Do You Support # of Individuls Capital Punishment? Yes 40 No 60 No Opinion 50 We are interested in determining whether the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 12-1. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals _____.

7.37776 9.34840 *5.99147* 7.81473

Excel's CHISQ.DIST function can be used to perform _____.

All of the answers are correct. a test for equality of population proportions a test for equality of population means *a goodness of fit test*

The F ratio in a completely randomized ANOVA is the ratio of _____.

MSE/MSTR MST/MSE *MSTR/MSE* MSE/MST

In factorial designs, the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as _____.

None of the answers is correct. *interaction* replication the main effect

Exhibit 11-7 Sample A Sample B s2 22 25 n 10 8 We want to test the hypothesis that population B has a smaller variance than population A. Refer to Exhibit 11-7. The null hypothesis _____.

None of the answers is correct. *should not be rejected* should be revised should be rejected

In a completely randomized design involving four treatments, the following information is provided. Treatment 1 Treatment 2 Treatment 3 Treatment 4 Sample size 50 18 15 17 Sample mean 32 38 42 48 The overall mean (the grand mean) for all treatments is _____.

None of the answers is correct. 37.0 *37.3* 40.0 48.0

Exhibit 13-6 Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 8 Within treatments (Error) 2 Total 100 ​ Refer to Exhibit 13-6. The conclusion of the test is that the means ____

None of the answers is correct. are equal *are not equal* may be equal

Exhibit 11-8 n = 23 H0: σ2 ≥ 66 s2 = 60 Ha: σ2 < 66 Refer to Exhibit 11-8. The null hypothesis _____.

None of the answers is correct. should be rejected *should not be rejected* should be revised

When an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (MSTR) is _____.

SSTR/k SSTR/(nT - 1) *SSTR/(k - 1)* SSTR/nT

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments. The following information is provided. ​ SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. The conclusion of the test is that the five means _____.

are equal may be equal *are not equal* None of the answers is correct.

Exhibit 12-6 The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. Political Party Support Democrats 100 Republicans 120 Independents 80 We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. The number of categories of outcomes per trial for a multinomial probability distribution is _____.

four or more five or more *three or more* two or more

Exhibit 12-6 The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. Political Party Support Democrats 100 Republicans 120 Independents 80 We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. Refer to Exhibit 12-6. This test for goodness of fit _____.

is a two-tailed test *is an upper-tail test* is a lower-tail test can be a lower-tail or upper-tail test

The sampling distribution for a goodness of fit test is the _____.

normal distribution Poisson distribution t distribution *chi-square distribution*

Exhibit 11-10 n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 Refer to Exhibit 11-10. At 95% confidence, the null hypothesis _____.

should be rejected *should not be rejected* None of the answers is correct. should be revised

Exhibit 11-4 n = 30 H0: σ2 = 500 s2 = 625 Ha: σ2 ≠ 500 Refer to Exhibit 11-4. The null hypothesis _____.

should be rejected should be revised *should not be rejected* None of the answers is correct.

To avoid the problem of not having access to tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with the _____.

smaller sample variance larger sample size *larger sample variance* smaller sample size

The sampling distribution of the ratio of two independent sample variances taken from normal populations with equal variances is a(n) _____ distribution.

t *F* χ2 normal

An important application of the chi-square distribution is _____.

testing for goodness of fit *All of the answers are correct.* testing for equality of three or more population proportions testing for the independence of two variables

An important application of the chi-square distribution is _____.

testing for the independence of two variables *All of the answers are correct.* testing for goodness of fit testing for equality of three or more population proportions

In the analysis of variance procedure (ANOVA), factor refers to _____.

the dependent variable the critical value of F *the independent variable* different levels of a treatment

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The null hypothesis for this ANOVA problem is _____.

μ1 = μ2 μ1 = μ2 = μ3 = μ4 *μ1 = μ2 = μ3* μ1 = μ2 = ... = μ12

Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 ​ Refer to Exhibit 13-2. The null hypothesis for this ANOVA problem is _____.

μ1 = μ2 = μ3 = μ4 = μ5 = μ6 *μ1 = μ2 = μ3 = μ4 = μ5* μ1 = μ2 = μ3 = μ4 μ1 = μ2 = ... = μ20

The degrees of freedom for a contingency table with 10 rows and 11 columns is _____.

110 100 *90* 21

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The χ2 values to be used for this interval estimation are _____.

16.151 and 40.113 -1.96 and 1.96 *14.573 and 43.195* 15.308 and 44.461

The degrees of freedom for a contingency table with 6 rows and 3 columns is _____.

18 6 15 *10*

Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.81 years. Recently, a sample of 10 students had a standard deviation of 2.1 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. Refer to Exhibit 11-1. The test statistic is _____.

2.1 3.28 14.2 *12.1*

Exhibit 12-1 Individuals in a random sample of 150 were asked whether they supported capital punishment. The following information was obtained. Do You Support # of Individuls Capital Punishment? Yes 40 No 60 No Opinion 50 We are interested in determining whether the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 12-1. The calculated value for the test statistic equals _____.

20 -2 2 *4*

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether the proportions have changed, a random sample of 300 students from ABC University was selected. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 12-4. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals _____.

*5.99* 7.80 1.645 19.6

Exhibit 12-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year's student body showed the following number of students in each class. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year. Refer to Exhibit 12-2. If the distribution is the same as the previous year, the expected frequency of seniors is _____.

*60* 64 68 20

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is _____.

*H0: σ2 ≥ 1.44* H0: σ ≤ 1.20 H0: s2 ≥ 1.44 H0: σ2 < 1.44

Exhibit 12-6 The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. Political Party Support Democrats 100 Republicans 120 Independents 80 We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. Refer to Exhibit 12-6. If the opinions of the individuals of the three groups are uniformly distributed, the expected frequency for each group is _____.

*None of the answers is correct.* 50 .50 .333

Exhibit 12-3 In order to determine whether a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Patients Cured Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether the medication was effective in curing the common cold. Refer to Exhibit 12-3. The test statistic is _____.

10.08 *54.02* 1.96 1.645

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether the proportions have changed, a random sample of 300 students from ABC University was selected. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 12-4. Based upon this test, what can be concluded?

*There is enough evidence to conclude that the proportions have not changed significantly.* The test is inconclusive. There is enough evidence to conclude that the proportions have changed significantly. None of the answers is correct.

The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30 bottles showed a standard deviation of .2. The p-value for the test is _____.

*between .025 and .05* between .05 and .01 .025 .05

The sampling distribution of the (n-1)s^2 quantity is the ____ --------- σ^2

*χ2 distribution* t distribution normal distribution F distribution

Exhibit 12-5 The table below gives beverage preferences for random samples of teens and adults. Beverage Teens Adults Total ---------------------------------------------------- Coffee 50 200 250 Tea 100 150 250 Soft drink 200 200 400 Other 50 50 100 -------------------------------------- 400 600 1,000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 12-5. The value of the test statistic for this test for independence is_____.

0 *62.5* 82.5 8.4

Exhibit 11-7 Sample A Sample B s2 22 25 n 10 8 We want to test the hypothesis that population B has a smaller variance than population A. Refer to Exhibit 11-7. The test statistic for this problem equals _____.

1.29 .77 *1.14* .88

Exhibit 12-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year's student body showed the following number of students in each class. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year. Refer to Exhibit 12-2. If the distribution is the same as the previous year, the expected number of freshmen is _____.

10 *90* 83 30

Exhibit 12-6 The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. Political Party Support Democrats 100 Republicans 120 Independents 80 We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. Refer to Exhibit 12-6. The number of degrees of freedom associated with this problem is _____.

299 *2* 300 3

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____.

3 and 30 *3 and 116* 4 and 30 3 and 119

Exhibit 11-7 Sample A Sample B s2 22 25 n 10 8 We want to test the hypothesis that population B has a smaller variance than population A. Refer to Exhibit 11-7. The null hypothesis is to be tested at the 5% level of significance. The critical value from the table is _____.

3.68 3.35 3.07 *3.29*

The 90% confidence interval estimate for a population standard deviation when a sample variance of 50 is obtained from a sample of 15 items is _____.

4.18 to 15.07 5.18 to 11.15 *5.44 to 10.32* 29.55 to 106.53

Exhibit 13-2 Source of Variation Sum ofSquares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 ​ Refer to Exhibit 13-2. The test statistic to test the null hypothesis equals _____.

432 28.8 4.17 *1.8*

Exhibit 11-9 n = 14 s = 20 H0: σ2 ≤ 500 Ha: σ2 ≥ 500 Refer to Exhibit 11-9. The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____.

5.009 and 24.736 23.685 5.629 and 26.119 *22.362*

Exhibit 11-5 n = 14 H0: σ2 ≤ 410 s = 20 Ha: σ2 > 410 Refer to Exhibit 11-5. The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____.

5.62872 and 26.119 23.6848 5.00874 and 24.7356 *22.3621*

Exhibit 12-3 In order to determine whether a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Patients Cured Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether the medication was effective in curing the common cold. Refer to Exhibit 12-3. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals _____.

5.99 *3.84* 9.34 7.81

Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounce. We are interested in testing to determine whether the variance of the population is significantly more than .003. Refer to Exhibit 11-3. The test statistic is _____.

500 31.2 1.2 *30*

In Excel, which of the following functions is used to conduct a hypothesis test (using the p-value) for a population variance?

CHI.INV *CHISQ.DIST* F-Test None of the answers is correct.

To avoid the problem of not having access to tables of the F distribution with values given for the lower tail when a two-tailed test is required, let the smaller sample variance be _____.

None of the answers is correct. the numerator of the test statistic *the denominator of the test statistic* at least 1

Excel's ____ function is used to perform a goodness of fit test.

TTEST NORM.S.DIST *CHISQ.DIST.RT* ZTEST

Exhibit 12-5 The table below gives beverage preferences for random samples of teens and adults. Beverage Teens Adults Total ---------------------------------------------------- Coffee 50 200 250 Tea 100 150 250 Soft drink 200 200 400 Other 50 50 100 -------------------------------------- 400 600 1,000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 12-5. What can be concluded from this test?

The test is inconclusive. There is not enough evidence to conclude that age and drink preference is dependent. None of the answers is correct. *There is enough evidence to conclude that age and drink preference is dependent.*

In order NOT to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be _____.

at least 10 less than 2 no more than 5 *at least 5*

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a _____.

contingency test probability test None of the answers is correct. *goodness of fit test*

In practice, the most frequently encountered hypothesis test about a population variance is a _____.

two-tailed test, with equal-size rejection regions *one-tailed test, with rejection region in upper tail* two-tailed test, with unequal-size rejection regions one-tailed test, with rejection region in lower tail

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is _____.

k - 1 dependent upon the statement of the null hypothesis n - 1 *number of rows minus 1 times number of columns minus 1*

Exhibit 11-8 n = 23 H0: σ2 ≥ 66 s2 = 60 Ha: σ2 < 66 Refer to Exhibit 11-8. The p-value is _____.

less than .10 less than .025 *greater than .10* less than .05

For an F distribution, the number of degrees of freedom for the numerator _____.

must be larger than the number of degrees for the denominator must be smaller than the number of degrees of freedom for the denominator *can be larger, smaller, or equal to the number of degrees of freedom for the denominator* must be equal to the number of degrees of freedom for the denominator

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the _____.

normal distribution t distribution *Z distribution* χ2 distribution

A population where each element of the population is assigned to one and only one of several classes or categories is a _____.

normal population Poisson population *multinomial population* None of the answers is correct.

Exhibit 11-10 n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 Refer to Exhibit 11-10. At 95% confidence, the null hypothesis _____.

should be revised should be rejected *should not be rejected* None of the answers is correct.

Exhibit 12-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year's student body showed the following number of students in each class. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year. Refer to Exhibit 12-2. The null hypothesis _____.

was designed wrong should be rejected None of the answers is correct. *should not be rejected*