Statistics 2101 - Dr. Wilson Spring 1996 Homework #9. Chapter 10 ========== 1. Suppose that you are interested in studies of heights of American men, a variable known to be approximately normally distributed in the population. Let us assume that the mean height in the population of American men (mu) is equal to 68 inches and the population standard deviation (sigma) is equal to 3.2 inches. Suppose now that you randomly draw one sample of N=100 midwestern American men, and you calculate the mean height of this sample as xbar = 67.4 inches and the standard deviation of the sample as s = 3.5 inches. Using these data, decide whether the average height of midwestern men is different from the average of the entire US adult male population (Use a level of significance equal to .05). a) State the Null and Alternative Hypotheses (using symbols). b) Specify the decision criterion and draw the rejection region. c) Compute the test statistic. d) Make a decision about the null hypothesis. In addition, state your conclusion in english. 2. Suppose that the population standard deviation (sigma) is actually 2.2 inches, and we decide to use a level of significance of .01 (Everything else remains the same). Redo problem # 1 using the new data, following steps a through d. 3. Frito-Lay corporation claims that their bags of Doritos tortilla chips contain 269.8 grams. To test their claim, I weighed the contents of eight packages of Doritos tortillas (Nacho cheese flavor) on a scale in my lab. The mean weight of this sample of Doritos bags was xbar= 270.39 grams, with a standard deviation of s = 0.52 gram. According to our data, is the claim that Doritos bags weigh 269.8 grams justified? (Use a significance level of .01). a) State the Null and Alternative Hypotheses (using symbols). b) Specify the decision criterion and draw the rejection region. c) Compute the test statistic. d) Make a decision about the null hypothesis. In addition, state your conclusion in english. 4. Suppose I ask you now the following question: Do Doritos bags weigh MORE than 269.8 grams. Using the data from problem # 3 answer this ONE-tailed question. Again, follow steps a through d. Chapter 11 ========== 5. Imagine being lost at sea, bobbing around in an orange life jacket. The Coast Guard sends out two kinds of observers to find you: fellow humans and pigeons. Each observer is successful; the search time in minutes for each observer is given in the table. Analyze the results and write a conclusion about the performance of the two types of observers. Humans Pigeons 45 31 63 24 39 20 a) Calculate the mean and standard deviation of each sample. b) State the Null and Alternative Hypotheses. c) What are the critical values of t? (Use alpha = .05) d) Compute the test statistic. e) Make a decision.