Tutorial 12

TUTORIAL 12 1. The following hypotheses are given: H 0 : σ 12 = σ 22 H 0 : σ 12 ≠ σ 22 A random sample of eight observations from the first population resulted in a standard deviation of 10.A random sample of six observations from the second population resulted in standard deviation of 7. At the 0.02 significance level, is there a difference in the variation of the two populations? 2. Random sample of five were selected from each of three populations. The sum of squares total was 100. The sum of squares due to the treatments was 40. a. Set up the null hypothesis and the alternate hypothesis b. What is the decision rule? Use 0.05 significance level c. Complete the ANOVA table. What is the value of F? d. What is your decision regarding the null hypothesis? 3. The following is a partial ANOVA table. Source

Sum of Square

Mean square

df

Treatment

2

Error Total

F

20 500

11

Complete the table and answer the following questions. Use the 0.05 significance level. a. How many treatment are there? b. What is the total sample size? c. What is the critical value of F? d. Write out the null and alternate hypotheses? e. What is you conclusion regarding the null hypotheses? 4. A consumer organization wants to know whether there are is the difference in the price of a particular toy at three different types of stores. The price of the toy was checked in a sample of five discount stores, five variety stores and five department stores. The result are shown below. Use the 0.05 significance level Discount 12 13 14 12 15

Variety 15 17 14 18 17

Department 19 17 16 20 19

5. A Physician who specializes in weight control has a three different diets she recommends. As an experiment, She randomly selected 15 patients and then assigned 5 to each diet. After three weeks the following weight losses, in pounds, were noted/

At the 0.05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets? Plan A 5 7 4 5 4

Plan B 6 7 7 5 6

6.

Plan C 7 8 9 8 9