1. The average McDonald's restaurant generates $2 million in sales each year with a standard deviation of 0.2. Alfonso wants to know if the average sales generated by McDonald's restaurants in California is different than the worldwide average. He surveys 33 restaurants in California and finds the following data (in millions of dollars): 1.8, 1.9, 2, 1.9, 2.3, 1.9, 1.8, 2, 2.2, 1.9, 2, 2, 2.2, 2.2, 1.8, 1.8, 2.3, 2.1, 2.2, 2, 2.2, 1.9, 2, 2.1, 2.1, 2, 2.3, 1.7, 2.2, 1.9, 1.7, 2.1, 2.1 Perform a hypothesis test using a 8% level of significance. Step 1: State the null and alternative hypotheses. H0:H0: ? p ? < > = Ha:Ha: ? p ? < > = (So we will be performing a Select an answer left-tailed right-tailed two-tailed test.) Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are Select an answer normally distributed t-distributed with distribution mean and distribution standard deviation . Step 3: Find the pp-value of the point estimate. P(P(? p' x ? )=P()=P(? z t ? )=)= pp-value== Step 4: Make a Conclusion About the null hypothesis. Since the pp-value== ? < ==, we Select an answer reject do not reject the null hypothesis.

• We cannot conclude that the mean sales of McDonald's restaurants in California differ from average McDonald's sales worldwide.
• We conclude that the mean sales of McDonald's restaurants in California differ from average McDonald's sales worldwide.

2. A mayor running for re-election claims that during his term, average municipal taxes have fallen by $300. A conscientious statistician wants to test this claim. He surveys 40 of his neighbors and finds that their taxes decreased (in dollars) as follows: 331, 215, 273, 299, 319, 274, 299, 313, 265, 277, 320, 237, 310, 286, 346, 320, 356, 304, 266, 300, 296, 253, 371, 266, 342, 289, 296, 260, 314, 335, 295, 280, 278, 355, 265, 354, 338, 280, 282, 336 The statistician assumes a population standard deviation of $33. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. ? p = __________ Step 2: Determine the Features of the Distribution of Point Estimates Using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are Select an answer normally distributed t-distributed with distribution mean and distribution standard deviation . Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P(? p' x ? _________ )=P(? z t ? __________ )= Step 4: Make a Conclusion About the Claim. What do you think? Based on the probability you calculated in step 3 of obtaining the point estimate, would you reject the claim?