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Public health advocates in all provinces and territories strongly believe that further price (tax) increases on cigarettes can be immensely effective in reducing the consumption of tobacco. A health researcher wants to compare the prices of a carton of 200 cigarettes among three western provinces - Alberta, British Columbia, and Saskatchewan. He randomly selects 5 stores that sell tobacco in each of the three provinces. The prices are given in the table below (all provincial and federal taxes including GST included) Price of a Carton of 200 Cigarettes Alberta British Columbia Saskatchewan $ 91.93 $ 97.04 $ 91 18 88 99 95.49 89.99 93.99 94.63 93.48 92.99 92.99 94.99 89.48 98.99 96.99 The health researcher wants to test if the mean price of a carton of 200 cigarettes is the same for all three provinces. Assuming that all the assumptions required to apply for the one-way ANOVA procedure hold true, answer the following questions. a. Which of the following is the correct pair of the null and alternative hypotheses? Choose the number that shows the correct pair. 1. HO : H1 = #2 = H3. H : Not all three means are equal 2. HO : 1 1 = #2 = H3 = H4 = #5. H : Not all means are equal 3. HO : #1 = H2. H1 : 17 # #2b. Which of the following distributions would you use to test the hypothesis in part (a)? Choose the number 1, 2 or 3. 1: t distribution 2. F distribution 3. x- distribution c. To test the null hypothesis in part (a) at a = 0.05 level of significance, what is the critical value of F?. Use the appropriate distribution table and express the value to two decimal places of accuracy. d. What is the calculated value of the test statistic? Express the value to two decimal places of accuracy. (Note: To save computational time, assume SSB # 47.7040 and SSW - 72.0048.) e. Based on your answers in part (c) and (d), will you reject the null hypothesis stated in part (a) at 5 % level of significance? Enter 1 or 2 to indicate the correct decision. 1. Do not reject HO. 2. Reject HO. f. Which of the following will be your conclusion of the test? Enter 1 or 2 to indicate the correct conclusion. 1. We can conclude that the mean price of cigarettes for all three provinces is the same. 2. There is sufficient evidence to indicate at least one of the three average cigarette prices is different from the others