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

A dietician wants to see if there is any difference in the effectiveness of three diets. Eighteen people were randomly chosen for the test. Then each individual was randomly assigned to one of the three diets. Below you are given the total amount of weight lost in six months by each person. Diet A Diet B Diet C 14 12 25 18 10 32 20 22 18 12 12 14 20 16 17 18 12 14 a. State the null and alternative hypotheses. b. Calculate the test statistic. c. What would you advise the dietician about the effectiveness of the three diets? Use a .05 level of significance.

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80.00 60.00 Sample mean \ 16.75 \ 16.25 Population standard deviation \ 1.00 \ 0.95 -Refer to Exhibit 10-8. The p-value is

In order to compare the life expectancies of three different brands of tires, ten tires of each brand were randomly selected and were subjected to standard wear testing procedures. Information regarding the three brands is shown below. Brand A Brand B Brand C Average mileage in 1000 miles) 37 38 33 Sample variance 3 4 2 Use the above data and test to see if the mean mileage for all three brands of tires is the same. Let α = 0.05. Use both the critical value and p-value approaches.

Test scores on a standardized test from samples of students from two universities are given below. UA UB Sample Size 28 41 Average Test Score 84 82 variance 64 100 Provide a 98% confidence interval estimate for the difference between the test scores of the two universities.

For testing the following hypothesis at 95% confidence, the null hypothesis will be rejected if Η0: μ1 - μ2 ≤ 0 Ηα: μ1 - μ2 > 0

In order to estimate the difference between the average yearly salaries of top managers in private and governmental organizations, the following information was gathered. Private Governmenta Sample Size 50 60 Sample Mean in \ 1,000s) 90 80 Sample Standard Deviation in \ 1,000s) 6 8 Develop an interval estimate for the difference between the average salaries of the two sectors. Let α = .05.

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 -Refer to Exhibit 10-9. The test statistic is

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 sum of squares within treatments SSE) is

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 95% confidence interval for the difference between the two population means is

For a two-tailed test at 98.5% confidence, Z =

Independent random samples taken at two local malls provided the following information regarding purchases by patrons of the two malls. Hamilton Place Eastgate Sample Size 85 93 Average Purchase \ 143 \ 150 Standard Deviation \ 22 \ 18 We want to determine whether or not there is a significant difference between the average purchases by the patrons of the two malls. a. Give the hypotheses for the above. b. Compute the test statistic. c. At 95% confidence, test the hypotheses.

We are interested in testing the following hypotheses. H0: μ1- μ2 = 0 Ha: μ1- μ2 ? 0 The test statistic Z is computed to be 1.85. The p-value for this test is

If we are interested in testing whether the mean of population 1 is significantly different from the mean of population 2, the correct null hypothesis is

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

Information regarding the ACT scores of samples of students in three different majors is given below. Major Management Finance Accounting 28 22 29 26 23 27 25 24 26 27 22 28 21 24 25 19 26 26 27 27 28 17 29 20 17 28 20 23 24 28 28 29 Sums 230 225 338 Means 23 25 26 Variances 18 6.75 933 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.

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 point estimate for the difference between the two sample means is

We are interested in testing the following hypotheses. H0: μ1­ μ2 = 0 Ha: μ1­ μ2 ≠ 0 The test statistic Z is computed to be 2.00. The p-value for this test is

In the analysis of variance procedure ANOVA), "factor" refers to

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

A potential investor conducted a 144 day survey in each theater in order to determine the difference between the average daily attendance at the North Mall and South Mall theaters. The North Mall Theater averaged 630 patrons per day; while the South Mall Theater averaged 598 patrons per day. From past information, it is known that the variance for North Mall is 1,000; while the variance for the South Mall is 1,304. Develop a 95% confidence interval for the difference between the average daily attendance at the two theaters.