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

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. For this problem, the degrees of freedom are computed to be 36. -Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is

Consider the following results for two samples randomly taken from two populations. a.Determine the degrees of freedom for the t distribution. b.Develop a 95% confidence interval for the difference between the two population means. c.Is there conclusive evidence that one population has a larger mean? Explain.

Exhibit 10-12 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. -Refer to Exhibit 10-12. The test statistic is

Exhibit 10-14 Part of an ANOVA table is shown below. -Refer to Exhibit 10-14. The number of degrees of freedom corresponding to between treatments is

The following information was obtained from matched samples regarding the productivity of four individuals using two different methods of production. Let d  Method 1  Method 2. Is there a significant difference between the productivity of the two methods? Let   0.05.

Exhibit 10-13 Part of an ANOVA table is shown below. -Refer to Exhibit 10-13. The mean square within treatments (MSE) is

Consider the following results for two samples randomly taken from two normal populations with equal variances. a.Develop a 95% confidence interval for the difference between the two population means. b.Is there conclusive evidence that one population has a larger mean? Explain.

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

Exhibit 10-13 Part of an ANOVA table is shown below. -Refer to Exhibit 10-13. The test statistic is

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. -Refer to Exhibit 10-2. The

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. a.Compute the overall sample mean. b.At   0.05, test to see if there is any significant difference in the average scores of the students from the three universities. Set up the complete ANOVA table (Note that the sample sizes are not equal.)

Random samples were selected from three populations. The data obtained are shown below. a.Compute the overall sample mean. b.At 90% confidence, test to see if there is a significant difference in the means of the three populations. Show the complete ANOVA table. Please note that the sample sizes are not equal.

In a completely randomized design involving three treatments, the following information is provided: The overall mean for all the treatments is

Information regarding the ACT scores of samples of students in three different majors is given below. 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.

In order to determine whether or not a driver's education course improves the scores on a driving exam, a sample of 6 students were given the exam before and after taking the course. The results are shown below. Let d  Score After - Score Before. a.Compute the test statistic. b.At 95% confidence using the p-value approach, test to see if taking the course actually increased scores on the driving exam.

In making three pairwise comparisons, what is the experiment-wise Type I error rate _ew if the comparison-wise Type I error rate  is .10?

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. -Refer to Exhibit 10-3. The point estimate for the difference between the means of the two populations is

Exhibit 10-14 Part of an ANOVA table is shown below. -Refer to Exhibit 10-14. If at 95% confidence we want to determine whether or not the means of the populations are equal, the p-value is

When developing an interval estimate for the difference between two sample means, with sample sizes of n₁ and n₂,

A survey was recently conducted to determine if consumers spend more on computer-related purchases via the Internet or store visits. Assume a sample of 8 respondents provided the following data on their computer-related purchases during a 30-day period. Using a .05 level of significance, can we conclude that consumers spend more on computer-related purchases by way of the Internet than by visiting stores?