Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. -\[\begin{array} { l r c c c c } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { p } \\ \text { Factor } & 3 & 13.500 & 4.500 & 5.17 & 0.011 \\ \text { Error } & 16 & 13.925 & 0.870 & & \\ \text { Total } & 19 & 27.425 & & & \end{array}\] What can you conclude about the equality of the population means?

A) Accept the null hypothesis since the p-value is less than the significance level. B) Reject the null hypothesis since the p-value is greater than the significance level. C) Reject the null hypothesis since the p-value is less than the significance level. D) Accept the null hypothesis since the p-value is greater than the significance level. A) Accept the null hypothesis since the p-value is less than the significance level. B) Reject the null hypothesis since the p-value is greater than the significance level. C) Reject the null hypothesis since the p-value is less than the significance level. D) Accept the null hypothesis since the p-value is greater than the significance level.

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. -The data below represent the weight losses for people on three different exercise programs. $\begin{array}{lll} \text { Exercise A}&\text { Exercise B}& \text {Exercise C }\\\hline 2.5 & 5.8 & 4.3 \\ 8.8 & 4.9 & 6.2 \\ 7.3 & 1.1 & 5.8 \\ 9.8 & 7.8 & 8.1 \\ 5.1 & 1.2 & 7.9 \end{array}$ At the 1% significance level, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs?

Test statistic: F = 1.491. Critical valu

Provide an appropriate response. -Fill in the missing entries in the following partially completed one-way ANOVA table. $\begin{array}{|l|r|r|l|c|} \hline \text { Source } & \text { df } & \text { SS } & \text { MS=SS/df } & \text { F-statistic } \\ \hline \text { Treatment } & 3 & & & 11.16 \\ \hline \text { Error } & & 13.72 & 0.686 & \\ \hline \text { Total } & & & & \\ \hline \end{array}$

A) $\begin{array}{|l|r|c|c|c|} \hline \text { Source } & \text { df } & \text { SS } & \text { MS=SS/df } & \text { F-statistic } \\ \hline \text { Treatment } & 3 & 0.184 & 0.061 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 13.90 & & \\ \hline \end{array}$ B) $\begin{array}{|l|r|c|c|c|} \hline \text { Source } & \text { df } & \text { SS } & \text { MS=SS/df } & \text { F-statistic } \\ \hline \text { Treatment } & 3 & 22.97 & 7.66 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 36.69 & & \\ \hline \end{array}$ C) $\begin{array}{|l|c|c|c|c|} \hline \text { Source } & \text { df } & \text { SS } & \text { MS=SS/df } & \text { F-statistic } \\ \hline \text { Treatment } & 3 & 48.80 & 16.27 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 62.52 & & \\ \hline \end{array}$ D) $\begin{array}{|l|c|c|c|c|} \hline \text { Source } & \text { df } & \text { SS } & \text { MS=SS/df } & \text { F-statistic } \\ \hline \text { Treatment } & 3 & 2.55 & 7.66 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 16.27 & & \\ \hline \end{array}$ A) $\begin{array}{|l|r|c|c|c|} \hline \text { Source } & \text { df } & \text { SS } & \text { MS=SS/df } & \text { F-statistic } \\ \hline \text { Treatment } & 3 & 0.184 & 0.061 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 13.90 & & \\ \hline \end{array}$ B) $\begin{array}{|l|r|c|c|c|} \hline \text { Source } & \text { df } & \text { SS } & \text { MS=SS/df } & \text { F-statistic } \\ \hline \text { Treatment } & 3 & 22.97 & 7.66 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 36.69 & & \\ \hline \end{array}$ C) $\begin{array}{|l|c|c|c|c|} \hline \text { Source } & \text { df } & \text { SS } & \text { MS=SS/df } & \text { F-statistic } \\ \hline \text { Treatment } & 3 & 48.80 & 16.27 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 62.52 & & \\ \hline \end{array}$ D) $\begin{array}{|l|c|c|c|c|} \hline \text { Source } & \text { df } & \text { SS } & \text { MS=SS/df } & \text { F-statistic } \\ \hline \text { Treatment } & 3 & 2.55 & 7.66 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 16.27 & & \\ \hline \end{array}$

The following data contains task completion times, in minutes, categorized according to the gender of the machine operator and the machine used. $\begin{array} { l } & \text { male}& \text {female }\\ \text {Machine 1 }&15,17&16,17\\ \text {Machine 2}&14,13&15,13\\ \text { Machine 3}&16,18&17,19\\ \end{array}$ Assume that two-way ANOVA is used to analyze the data. How are the ANOVA results affected if the first sample value in the first cell is changed to 30 minutes?

If the first sample value is changed to

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. -\[\begin{array} { l r c c c c } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Factor } & 3 & 13.500 & 4.500 & 5.17 & 0.011 \\ \text { Error } & 16 & 13.925 & 0.870 & & \\ \text { Total } & 19 & 27.425 & & & \end{array}\] Identify the value of the test statistic.

A) 13.500 B) 0.011 C) 5.17 D) 4.500 A) 13.500 B) 0.011 C) 5.17 D) 4.500

The following data contains task completion times, in minutes, categorized according to the gender of the machine operator and the machine used. $\begin{array}{lrl} & \text { Male } & \text { Female } \\ \text { Machine 1 } & 15,17 & 16,17 \\ \text { Machine 2 } & 14,13 & 15,13 \\ \text { Machine 3 } & 16,18 & 17,19 \end{array}$ Assume that two-way ANOVA is used to analyze the data. How are the ANOVA results affected if 5 minutes is added to each completion time?

The ANOVA results are not affected by ad

The following table entries are the times in seconds for three different drivers racing on four different tracks. Assuming no effect from the interaction between driver and track, test the claim that the three drivers have the same mean time. Use a 0.05 significance level. $\begin{array}{c|cccc} & \text { Track 1 } & \text { Track 2 } & \text { Track 3 } & \text { Track 4 } \\ \hline \text { Driver 1 } & 72 & 70 & 68 & 71 \\ \text { Driver 2 } & 74 & 71 & 66 & 72 \\ \text { Driver 3 } & 76 & 69 & 64 & 70 \end{array}$ \[\begin{array} { l r c l r c } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { p } \\ \text { Driver } & 2 & 2 & 1 & 0.33 & 0.729 \\ \text { Track } & 3 & 98.25 & 32.75 & 10.92 & 0.00763 \\ \text { Error } & 6 & 18 & 3 & & \\ \text { Total } & 11 & 118.25 & & & \end{array}\]

@#LAT-DLM& : There is no driver effect. @#LAT-DLM& : There i

The following table entries are the times in seconds for three different drivers racing on four different tracks. Assuming no effect from the interaction between driver and track, test the claim that the track has no effect on the time. Use a 0.05 significance level. \[\begin{array}{l} \begin{array} { c | c c c c } & \text { Track 1 } & \text { Track 2 } & \text { Track 3 } & \text { Track 4 } \\ \hline \text { Driver 1 } & 72 & 70 & 68 & 71 \\ \text { Driver 2 } & 74 & 71 & 66 & 72 \\ \text { Driver 3 } & 76 & 69 & 64 & 70 \end{array}\\\\ \begin{array} { l r c l r l } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { p } \\ \text { Driver } & 2 & 2 & 1 & 0.33 & 0.729 \\ \text { Track } & 3 & 98.25 & 32.75 & 10.92 & 0.00763 \\ \text { Error } & 6 & 18 & 3 & & \\ \text { Total } & 11 & 118.25 & & & \end{array} \end{array}\]

@#LAT-DLM& : There is no track effect. @#LAT-DLM&

Exam 12: Analysis of Variance

A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow. Employee A B C Machine II 16,18,19 15,17,20 14,18,16 II 20,27,29 25,28,27 29,28,26 III 15,18,17 16,16,19 13,17,16 ANALYSIS OF VARIANCE ITEMS SOURCE DF SS MS MACHINE 2 588.74 294.37 EMPLOYEE 2 2.07 1.04 INTERACTION 4 15.48 3.87 ERROR 18 98.67 5.48 TOTAL 26 704.96 Using a 0.05 significance level, test the claim that the interaction between employee and machine has no effect on the number of items produced.

Free

(Essay)

4.9/5

(35)

Question 1

Correct Answer:

Verified

$\mathrm { H } _ { 0 } :$ There is no interaction effect.
$\mathrm { H } _ { 1 }$ : There is an interaction effect.
Test statistic: $\mathrm { F } = 0.7062$ . Critical value: $\mathrm { F } = 2.9277$ .
Fail to reject the null hypothesis. There does not appear to be an interaction effect.

The following data contains task completion times, in minutes, categorized according to the gender of the machine operator and the machine used. Male Female Machine 1 15,17 16,17 Machine 2 14,13 15,13 Machine 3 16,18 17,19 Assume that two-way ANOVA is used to analyze the data. How are the ANOVA results affected if the times are converted to hours?

Free

(Essay)

4.7/5

(35)

Question 2

Correct Answer:

Verified

The ANOVA results are not affected by converting the times to hours. The null hypothesis of no interaction between machine and gender is not rejected since the P-value is 0.946. The null hypothesis of no effect from machine is rejected since the P-value is 0.013. The null hypothesis of no effect from gender is not rejected since the P-value is 0.382.

Provide an appropriate response. - $\text { The test statistic for one-way ANOVA is } F = \frac { \text { variance between samples } } { \text { variance within samples } } \text {. Describe variance within samples and }$ variance between samples. What relationship between variance within samples and variance between samples would result in the conclusion that the value of F is significant?

Free

(Essay)

5.0/5

(38)

Question 3

Correct Answer:

Verified

Variance between samples measures the variation between the sample means, that is the variation due to the treatment. The variance within the samples depends solely on the sample variances. The F ratio compares the two. If the F ratio is relatively close to 1, the two variances are about the same, and we conclude that there are no significant differences among the sample means. When the value of F is excessively large (that is, greater than 1), we conclude that the variation among the samples is not the same and that the means are not equal

Provide an appropriate response. -When using statistical software packages, the critical value is typically not given. What method is used to determine whether you reject or fail to reject the null hypothesis?

(Essay)

4.8/5

(33)

Question 4

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. - Source DF SS MS F p Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425 What can you conclude about the equality of the population means?

(Multiple Choice)

4.9/5

(24)

Question 5

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. -Random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below. Model A Model B Model C Model D 23 28 30 25 25 26 28 26 24 29 32 25 26 30 27 28 Test the claim that the four different models have the same population mean. Use a significance level of 0.05.

(Essay)

4.9/5

(39)

Question 6

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. -The data below represent the weight losses for people on three different exercise programs. Exercise A Exercise B Exercise C 2.5 5.8 4.3 8.8 4.9 6.2 7.3 1.1 5.8 9.8 7.8 8.1 5.1 1.2 7.9 At the 1% significance level, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs?

(Essay)

4.9/5

(38)

Question 7

Provide an appropriate response. -Fill in the missing entries in the following partially completed one-way ANOVA table. Source df SS MS=SS/df F-statistic Treatment 3 11.16 Error 13.72 0.686 Total

(Multiple Choice)

4.8/5

(33)

Question 8

The following data contains task completion times, in minutes, categorized according to the gender of the machine operator and the machine used. male female Machine 1 15,17 16,17 Machine 2 14,13 15,13 Machine 3 16,18 17,19 The ANOVA results lead us to conclude that the completion times are not affected by an interaction between machine and gender, and the times are not affected by gender, but they are affected by the machine. Change the table entries so that there is no effect from the interaction between machine and gender, but there is an effect from the gender of the operator.

(Essay)

4.9/5

(29)

Question 9

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. -At the 0.025 significance level, test the claim that the four brands have the same mean if the following sample results have been obtained. brandA brand B brand C brand D 15 20 21 15 25 17 22 15 21 22 20 14 23 23 19 23 22 18 22 20 28 28

(Essay)

4.8/5

(25)

Question 10

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. - Source DF SS MS F p Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80 Identify the p-value.

(Multiple Choice)

4.7/5

(36)

Question 11

The following data contains task completion times, in minutes, categorized according to the gender of the machine operator and the machine used. male female Machine 1 15,17 16,17 Machine 2 14,13 15,13 Machine 3 16,18 17,19 Assume that two-way ANOVA is used to analyze the data. How are the ANOVA results affected if the first sample value in the first cell is changed to 30 minutes?

(Essay)

4.9/5

(35)

Question 12

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. - Source DF SS MS F P Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425 Identify the value of the test statistic.

(Multiple Choice)

4.9/5

(36)

Question 13

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. - Source DF SS MS F p Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425 Find the critical value.

(Multiple Choice)

4.9/5

(39)

Question 14

The following data shows the yield, in bushels per acre, categorized according to three varieties of corn and three different soil conditions. Assume that yields are not affected by an interaction between variety and soil conditions, and test the null hypothesis that variety has no effect on yield. Use a 0.05 significance level. Plot 1 Plot 2 Plot 3 Variety 1 156,167, 162,160, 145,151 170,162 169,168 148,155 Variety 2 172,176, 179,186, 161,162 166,179 160,176 165,170 Variety 3 175,157, 178,170, 169,165 179,178 172,174 170,169

(Essay)

4.8/5

(37)

Question 15

The following data contains task completion times, in minutes, categorized according to the gender of the machine operator and the machine used. Male Female Machine 1 15,17 16,17 Machine 2 14,13 15,13 Machine 3 16,18 17,19 Assume that two-way ANOVA is used to analyze the data. How are the ANOVA results affected if 5 minutes is added to each completion time?

(Essay)

4.9/5

(32)

Question 16

The following table entries are the times in seconds for three different drivers racing on four different tracks. Assuming no effect from the interaction between driver and track, test the claim that the three drivers have the same mean time. Use a 0.05 significance level. Track 1 Track 2 Track 3 Track 4 Driver 1 72 70 68 71 Driver 2 74 71 66 72 Driver 3 76 69 64 70 Source DF SS MS F p Driver 2 2 1 0.33 0.729 Track 3 98.25 32.75 10.92 0.00763 Error 6 18 3 Total 11 118.25

(Essay)

4.9/5

(33)

Question 17

The following data shows annual income, in thousands of dollars, categorized according to the two factors of gender and level of education. Assume that incomes are not affected by an interaction between gender and level of education, and test the null hypothesis that level of education has no effect on income. Use a 0.05 significance level. Female Male High school 23,27,24,26 25,26,22,24 College 28,36,31,33 35,32,39,28 Advanced degree 41,38,43,49 35,50,47,44

(Essay)

4.7/5

(38)

Question 18

The following table entries are the times in seconds for three different drivers racing on four different tracks. Assuming no effect from the interaction between driver and track, test the claim that the track has no effect on the time. Use a 0.05 significance level. Track 1 Track 2 Track 3 Track 4 Driver 1 72 70 68 71 Driver 2 74 71 66 72 Driver 3 76 69 64 70 Source DF SS MS F p Driver 2 2 1 0.33 0.729 Track 3 98.25 32.75 10.92 0.00763 Error 6 18 3 Total 11 118.25

(Essay)

4.7/5

(41)

Question 19

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. - Source DF SS MS F p Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80 Find the critical value.

(Multiple Choice)

5.0/5

(26)

Question 20

Provide an appropriate response. -When using statistical software packages, the critical value is typically not given. What method is used to determine whether you reject or fail to reject the null hypothesis?

Provide an appropriate response. -Fill in the missing entries in the following partially completed one-way ANOVA table. Source df SS MS=SS/df F-statistic Treatment 3 11.16 Error 13.72 0.686 Total

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Multinomial Experiments and Contingency Tables

Nonparametric Statistics

Statistical Process Control

Filters