Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. \[\begin{array}{l} & \text { Today } & \text { Five Years Ago } \\ \overline { \mathrm { x } } & 82.0 & 88 \\ \sigma ^ { 2 } & 112.5 & 54 \\ \mathrm { n } & 45.0 & 36 \end{array}\] \[\begin{array}{cc} \text { Today } & \text { Five Years Ago }\\ 82.0 & 88 \\ 112.5 & 54 \\ 45.0 & 36 \end{array}\] $\begin{array}{cc} \text { Today }&\text { Five Years Ago }\\ 82.0 & 88 \\ 112.5 & 54 \\ 45.0 & 36 \end{array}$ n -Refer to Exhibit 10-3. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? Use a .05 level of significance.)

A) There is a statistically significant difference in the average final examination scores between the two classes. B) There is no statistically significant difference in the average final examination scores between the two classes. C) It is impossible to make a decision on the basis of the information given. D) There is a difference, but it is not significant. A) There is a statistically significant difference in the average final examination scores between the two classes. B) There is no statistically significant difference in the average final examination scores between the two classes. C) It is impossible to make a decision on the basis of the information given. D) There is a difference, but it is not significant.

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. \[\begin{array} { l c c } & \text { Sample } 1 & \text { Sample 2 } \\ \text { Sample Mean } & 45 & 42 \\ \text { Sanple Variance } & 85 & 90 \\ \text { Sample Size } & 10 & 12 \end{array}\] -Refer to Exhibit 10-4. The degrees of freedom for the t-distribution are

A) 22 B) 23 C) 24 D) 19 A) 22 B) 23 C) 24 D) 19

Exhibit 10-5 The following information was obtained from matched samples. $\begin{array}{ccc}\text { Individual }&\text { Method } 1&\text { Method } 2\\ 1 & 7 & 5 \\ 2 & 5 & 9 \\ 3 & 6 & 8 \\ 4 & 7 & 7 \\ 5 & 5 & 6 \end{array}$ -Refer to Exhibit 10-5. The 95% confidence interval for the difference between the two population means is

A) -3.776 to 1.776 B) -2.776 to 2.776 C) -1.776 to 2.776 D) 0 to 3.776 A) -3.776 to 1.776 B) -2.776 to 2.776 C) -1.776 to 2.776 D) 0 to 3.776

In a completely randomized design involving three treatments, the following information is provided: $\begin{array}{llcc}&\text { Treatment } 1&\text { Treatment } 2&\text { Treatment } 3\\ \text { Sample Size } & 5 & 10 & 5 \\ \text { Sample Mean } & 4 & 8 & 9 \end{array}$ The overall mean for all the treatments is

A) 7.00 B) 6.67 C) 7.25 D) 4.89 A) 7.00 B) 6.67 C) 7.25 D) 4.89

Exhibit 10-14 The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations. \[\begin{array} { l c c } \begin{array} { l } \text { Source of } \\ \text { Variation } \end{array} & \begin{array} { c } \text { Sum of } \\ \text { Squares } \end{array} & \begin{array} { c } \text { Degrees of } \\ \text { Freedom } \end{array} \\ \text { Between Treatments } & 64 & \\ \text { Error Within Treatments) } & 96 & \end{array}\] -Refer to Exhibit 10-14. The number of degrees of freedom corresponding to between treatments is

A) 12 B) 2 C) 3 D) 4 A) 12 B) 2 C) 3 D) 4

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. \[\begin{array} { c c c } \text { Worker } & \text { Before } & \text { After } \\ 1 & 20 & 22 \\ 2 & 25 & 23 \\ 3 & 27 & 27 \\ 4 & 23 & 20 \\ 5 & 22 & 25 \\ 6 & 20 & 19 \\ 7 & 17 & 18 \end{array}\] -Refer to Exhibit 10-2. The null hypothesis to be tested is H0: ?d = 0. The test statistic is

A) -1.96 B) 1.96 C) 0 D) 1.645 A) -1.96 B) 1.96 C) 0 D) 1.645

Exhibit 10-5 The following information was obtained from matched samples. $\begin{array}{ccc}\text { Individual }&\text { Method } 1&\text { Method } 2\\ 1 & 7 & 5 \\ 2 & 5 & 9 \\ 3 & 6 & 8 \\ 4 & 7 & 7 \\ 5 & 5 & 6 \end{array}$ -Refer to Exhibit 10-5. The point estimate for the difference between the means of the two populations Method 1 - Method 2) is

A) -1 B) 0 C) -4 D) 2 A) -1 B) 0 C) -4 D) 2

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. \[\begin{array} { c c c } \text { Worker } & \text { Before } & \text { After } \\ 1 & 20 & 22 \\ 2 & 25 & 23 \\ 3 & 27 & 27 \\ 4 & 23 & 20 \\ 5 & 22 & 25 \\ 6 & 20 & 19 \\ 7 & 17 & 18 \end{array}\] -Refer to Exhibit 10-2. The point estimate for the difference between the means of the two populations is

A) -1 B) -2 C) 0 D) 1 A) -1 B) -2 C) 0 D) 1

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. \[\begin{array}{l} & \text { Today } & \text { Five Years Ago } \\ \overline { \mathrm { x } } & 82.0 & 88 \\ \sigma ^ { 2 } & 112.5 & 54 \\ \mathrm { n } & 45.0 & 36 \end{array}\] \[\begin{array}{cc} \text { Today } & \text { Five Years Ago }\\ 82.0 & 88 \\ 112.5 & 54 \\ 45.0 & 36 \end{array}\] $\begin{array}{cc} \text { Today }&\text { Five Years Ago }\\ 82.0 & 88 \\ 112.5 & 54 \\ 45.0 & 36 \end{array}$ n -Refer to Exhibit 10-3. The test statistic for the difference between the two population means is

A) -.47 B) -.65 C) -1.5 D) -3 A) -.47 B) -.65 C) -1.5 D) -3

In order to test to see if there is any significant difference in the mean number of units produced per week by each of three production methods, the following data were collected. Please note that the sample sizes are not equal.) $\begin{array}{lll}\text { Method I }&\text { Method II }&\text { Method III }\\ 182 & 170 & 162 \\ 170 & 192 & 166 \\ 179 & 190 & \end{array}$ a. Compute . b. At the α = 0.05 level of significance, is there any difference in the mean number of units produced per week by each method? Show the complete ANOVA table. Use both the critical and p-value approaches.

a. 176.375 @#IMG-DLM& F = 3.154; p-valu

Information regarding random samples of annual salaries in thousands of dollars) of doctors in three different specialties is shown below. \[\begin{array} { l c c c } & \text { Pediatrics } & \text { Radiology } & \text { Pathology } \\ \text { Sample size } & 12 & 10 & 11 \\ \text { Average salary } & 120 & 186 & 240 \\ \text { Sample variance } & 16 & 18 & 20 \end{array}\] a. Compute the overall mean . b. State the null and alternative hypotheses to be tested. c. Show the complete ANOVA table for this test including the test statistic. d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude? e. Determine the p-value and use it for the test.

a. 180 b. Ho: There is no significant di

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. \[\begin{array} { l c c } & \text { Male } & \text { Female } \\ \text { Sample Size } & 64 & 36 \\ \text { Sample Mean Salary in } \$ 1,000) & 44 & 41 \\ \text { Population Variance } \sigma^{2} \text { ) } & 128 & 72 \end{array}\] -Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations is

A) -28 B) 3 C) 4 D) -4 A) -28 B) 3 C) 4 D) -4

Exam 10: Comparisons Involving Means, Experimental Design, and Analysis of Variance

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 82.0 88 112.5 54 45.0 36 Today Five Years Ago 82.0 88 112.5 54 45.0 36 Today Five Years Ago 82.0 88 112.5 54 45.0 36 n -Refer to Exhibit 10-3. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? Use a .05 level of significance.)

(Multiple Choice)

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Question 101

The manager of Ahmadi Corporation, wants to determine whether or not the type of work schedule for her employees has any effect on their productivity. She has selected 15 production employees at random and then randomly assigned 5 employees to each of the 3 proposed work schedules. The following table shows the units of production per week) under each of the work schedules. Work Schedule Treatments) Schedule 1 Schedule 2 Schedule 3 50 60 75 60 65 75 70 65 55 40 58 40 45 57 55 a. Compute the overall sample mean . b. At 95% confidence, determine if there is a significant difference in the mean weekly units of production for the three types of work schedules.

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Question 102

Exhibit 10-10 SSTR = 6,750 H0: μ1=μ2=μ3=μ4 SSE = 8,000 Ha: at least one mean is different nT = 20 -Refer to Exhibit 10-10. The null hypothesis

(Multiple Choice)

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Question 103

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sanple Variance 85 90 Sample Size 10 12 -Refer to Exhibit 10-4. The degrees of freedom for the t-distribution are

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Question 104

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 -Refer to Exhibit 10-5. The 95% confidence interval for the difference between the two population means is

(Multiple Choice)

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Question 105

In a completely randomized design involving three treatments, the following information is provided: Treatment 1 Treatment 2 Treatment 3 Sample Size 5 10 5 Sample Mean 4 8 9 The overall mean for all the treatments is

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Question 106

Exhibit 10-14 The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Between Treatments 64 Error Within Treatments) 96 -Refer to Exhibit 10-14. The number of degrees of freedom corresponding to between treatments is

(Multiple Choice)

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Question 107

If we are interested in testing whether the mean of items in population 1 is significantly smaller than the mean of items in population 2, the

(Multiple Choice)

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Question 108

In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is

(Multiple Choice)

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Question 109

If the p-value is larger than 1,

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Question 110

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 -Refer to Exhibit 10-2. The null hypothesis to be tested is H0: ?d = 0. The test statistic is

(Multiple Choice)

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Question 111

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 -Refer to Exhibit 10-5. The point estimate for the difference between the means of the two populations Method 1 - Method 2) is

(Multiple Choice)

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Question 112

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 -Refer to Exhibit 10-2. The point estimate for the difference between the means of the two populations is

(Multiple Choice)

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Question 113

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 82.0 88 112.5 54 45.0 36 Today Five Years Ago 82.0 88 112.5 54 45.0 36 Today Five Years Ago 82.0 88 112.5 54 45.0 36 n -Refer to Exhibit 10-3. The test statistic for the difference between the two population means is

(Multiple Choice)

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Question 114

In order to test to see if there is any significant difference in the mean number of units produced per week by each of three production methods, the following data were collected. Please note that the sample sizes are not equal.) Method I Method II Method III 182 170 162 170 192 166 179 190 a. Compute . b. At the α = 0.05 level of significance, is there any difference in the mean number of units produced per week by each method? Show the complete ANOVA table. Use both the critical and p-value approaches.

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Question 115

The mean square is the sum of squares divided by

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Question 116

Information regarding random samples of annual salaries in thousands of dollars) of doctors in three different specialties is shown below. Pediatrics Radiology Pathology Sample size 12 10 11 Average salary 120 186 240 Sample variance 16 18 20 a. Compute the overall mean . b. State the null and alternative hypotheses to be tested. c. Show the complete ANOVA table for this test including the test statistic. d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude? e. Determine the p-value and use it for the test.

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Question 117

Information regarding the ACT scores of samples of students in four different majors is given below. Majors Management Marketing Finance Accounting 29 22 29 28 27 22 27 26 21 25 27 25 28 26 28 20 22 27 24 21 28 20 20 19 28 23 20 27 23 25 30 24 28 27 29 21 24 28 23 29 27 31 27 24 Sums 318 245 234 312 Means 26.50 24.50 26.00 24.00 Variances 10.09 6.94 14.50 9.00 a. Set up the ANOVA table for this problem. b. At 95% confidence test to determine whether there is a significant difference in the means of the three populations.

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Question 118

The following information shows the yearly salaries in $1,000) of samples of physicians for 2013 and 2012. 1) 2) Year 2013 Year 2012 Sample Size 280 244 Sample Mean 790 685 Population Standard Deviation o) 100 110 We want to perform a test to determine if there has been a significant increase in the salaries of physicians. In your computations, please use "1" to represent year 2013. a. State the null and alternative hypotheses to be tested. H0: Ha: b. Compute the test statistic. c. The null hypothesis is to be tested at 95% confidence. Determine the critical value from the table. d. What do you conclude? Fully explain and answer the question. e. Compute the p-value.

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Question 119

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary in \ 1,000) 44 41 Population Variance ) 128 72 -Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations is

(Multiple Choice)

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Question 120

Exhibit 10-10 SSTR = 6,750 H0: μ1=μ2=μ3=μ4 SSE = 8,000 Ha: at least one mean is different nT = 20 -Refer to Exhibit 10-10. The null hypothesis

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sanple Variance 85 90 Sample Size 10 12 -Refer to Exhibit 10-4. The degrees of freedom for the t-distribution are

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 -Refer to Exhibit 10-5. The 95% confidence interval for the difference between the two population means is

In a completely randomized design involving three treatments, the following information is provided: Treatment 1 Treatment 2 Treatment 3 Sample Size 5 10 5 Sample Mean 4 8 9 The overall mean for all the treatments is

If we are interested in testing whether the mean of items in population 1 is significantly smaller than the mean of items in population 2, the

In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is

If the p-value is larger than 1,

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 -Refer to Exhibit 10-5. The point estimate for the difference between the means of the two populations Method 1 - Method 2) is

The mean square is the sum of squares divided by

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