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

Random samples were selected from three populations. The data obtained are shown below. Please note that the sample sizes are not equal. Treatment 1 Treatment 2 Treatment 3 45 31 39 41 34 35 37 35 40 40 40 42 a. Compute the overall mean . b. At 95% confidence, test to see if there is a significant difference among the means.

Nancy, Inc. has three stores located in three different areas. Random samples of the sales of the three stores In $1,000) are shown below. Store 1 Store 2 Store 3 46 34 33 47 36 31 45 35 35 42 39 45 a. Compute the overall mean . b. At 95% confidence, test to see if there is a significant difference in the average sales of the three stores.

Exhibit 10-13 Part of an ANOVA table is shown below. Source of Sum of Degrees Mean Variation Squares of Freedom Square F Between Treatments 64 8 Within Treatments 2 Error Total 100 -Refer to Exhibit 10-13. The mean square between treatments MSTR) is

Individuals were randomly assigned to three different production processes. The hourly units of production for the three processes are shown below. Production Process Process 1 Process 2 Process 3 33 33 28 30 35 36 28 30 30 29 38 34 Use the analysis of variance procedure with α = 0.05 to determine if there is a significant difference in the mean hourly units of production for the three types of production processes. Use both the critical and p-value approaches.

The following data present the number of computer units sold per day by a sample of 6 salespersons before and after a bonus plan was implemented. sales person Before After 1 3 6 2 7 5 3 6 6 4 8 7 5 7 8 6 9 8 At 95% confidence, test to see if the bonus plan was effective. That is, did the bonus plan actually increase sales? Let d = Before - After.

Three universities administer the same comprehensive examination to the recipients of MS degrees in psychology. From each institution, a random sample of MS recipients was selected, and these recipients were then given the exam. The following table shows the scores of the students from each university. Note that the sample sizes are not equal. University A University B University C 89 60 82 95 95 70 75 89 90 92 80 79 99 66 90 a. Compute the overall mean . b. At α = 0.01, test to see if there is any significant difference in the average scores of the students from the three universities. Use both the critical value and p-value approaches.

Three different models of automobiles A, B, and C) were compared for gasoline consumption. For each model of car, fifteen cars were randomly selected and subjected to standard driving procedures. The average miles/gallon obtained for each model of car and sample standard deviations are shown below. Car A Car B Car C Average Mile/Gallon 42 49 44 Sample Standard Deviation 4 5 3 Use the above data and test to see if the mean gasoline consumption for all three models of cars is the same. Let α = 0.05, and use both the critical and p-value approaches.

The following information was obtained from matched samples regarding the productivity of four individuals using two different methods of production. Individual Method 1 Method 2 1 6 8 2 9 5 3 7 6 4 7 5 5 8 6 6 9 5 7 6 3 Let d = Method 1 - Method 2. Is there a significant difference between the productivity of the two methods? Let α = 0.05.

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

Exhibit 10-7 In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. Sample size Duntown Stare North Mall atare Simple mean 25 20 Sample standard deviation $\$ 9$ 40 1 -Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with let n1 be the size of sample 1 and n2 the size of sample 2)

Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the

The heating bills for a selected sample of houses using various forms of heating are given below values are in dollars). Gas Heated Homes Central Electric Heat Pump 83 90 81 80 88 83 82 87 80 83 82 82 82 83 79 At α = 0.05, test to see if there is a significant difference among the average bills of the homes. Use both the critical and p-value approaches.

In order to estimate the difference between the average daily sales of two branches of a department store, the following data has been gathered. Downtown Store North Mall Store Sample size =23 days =26 days Sample mean in \ 1,000) =37 =34 Sample standard deviation in \ 1,000) =4 =5 a. Determine the point estimate of the difference between the means. b. Determine the degrees of freedom for this interval estimation. c. Compute the margin of error. d. Develop a 95% confidence interval for the difference between the two population means.

We are interested in testing the following hypotheses. H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0 The test statistic Z is computed to be 2.83. The p-value for this test is

In hypothesis testing if the null hypothesis is rejected,

Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the

A potential investor conducted a 49 day survey in two theaters in order to determine the difference between the average daily attendance at North Mall and South Mall Theaters. The North Mall Theater averaged 720 patrons per day with a variance of 100; while the South Mall Theater averaged 700 patrons per day with a variance of 96. Develop an interval estimate for the difference between the average daily attendance at the two theaters. Use a confidence coefficient of 0.95.

Exhibit 10-11 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments a total of 65 observations). The following information is provided. SSTR = 200 Sum Square Between Treatments) SST = 800 Total Sum Square) -Refer to Exhibit 10-11. The test statistic is

In order to test the following hypotheses at an α level of significance, H0: μ1- μ2 ≤ 0 Ha: μ1- μ2 > 0 The null hypothesis will be rejected if the test statistic Z is