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The manager of a restaurant in a large city claims that waiters working in all restaurants in his city eart an average of \(\$ 150\) or more in tips per week. A random sample of 25 waiters selected from restaurants of this city yielded a mean of \(\$ 139\) in tips per week with a standard deviation of \(\$ 28\). Assume that the weekly tips for all waiters in this city have a normal distribution a. Using a \(1 \%\) significance level, can you conclude that the manager's claim is true? Use both approaches b. What is the Type I error in this exercise? Explain. What is the probability of making such an error'

The manager of a service station claims that the mean amount spent on gas by its customers is $$\$ 15.90$$ per visit. You want to test if the mean amount spent on gas at this station is different from $$\$ 15.90$$ per visit. Briefly explain how you would conduct this test when \(\sigma\) is not known. \(9.73\) A tool manufacturing company claims that its top-of-the-line machine that is used to manufacture bolts produces an average of 88 or more bolts per hour. A company that is interested in buying this machine wants to check this claim. Suppose you are asked to conduct this test. Briefly explain how you would do so when \(\sigma\) is not known.

In each of the following cases, do you think the sample size is large enough to use the normal distribution to make a test of hypothesis about the population proportion? Explain why or why not. a. \(n=40\) and \(p=.11\) b. \(n=100\) and \(p=.7\) c. \(n=80 \quad\) and \(\quad p=.05\) d. \(n=50\) and \(p=.14\)

For each of the following examples of tests of hypothesis about the population proportion, show the rejection and nonrejection regions on the graph of the sampling distribution of the sample proportion. a. A two-tailed test with \(\alpha=.05\) b. A left-tailed test with \(\alpha=.02\) c. A right-tailed test with \(\alpha=.025\)

food company is planning to market a new type of frozen yogurt. However, before marketing thit yogurt, the company wants to find what percentage of the people like it. The company's management has decided that it will market this yogurt only if at least \(35 \%\) of the people like it. The company's researcl department selected a random sample of 400 persons and asked th taste this yogurt. Of these 400 persons, 112 said they liked a. Testing at a \(2.5 \%\) significance level, can you conclude that the company should market this yogurt b. What will your decision be in part a if the probability of making a Type I error is zero? Explain Make the test of part a using the \(p\) -value approach.min