Question 1: (Fill in the blanks )

The average McDonald's restaurant generates $2.3 million in sales each year with a standard deviation of 3.2. Alan wants to know if the average sales generated by McDonald's restaurants in North Carolina is different than the worldwide average. He surveys 15 restaurants in North Carolina and finds the following data {in millions of dollars]: 2.3, 2.2, 2.3, 2.3, 2.5, 2.3, 2.3, 2.2, 2.3, 2.9, 2.9, 2.3, 2.5, 2.4, 2.3 Perform a hypothesis test using a 295 level of significance. Step 1: State the null and alternative hypotheses. {So we will be performing a ovatailed v test.} Step 2: Assuming the null hypothesis is true,, determine the features of the distribution of point estimates using the Central Limit 111eorem. By the Central Limit Theorem, we know that the point estimates are with distribution mean :1 and distribution standard deviation :1. Step 3: Find the p-value of the point estimate. P :11 ll-:1} = S p-value = :l Step 4: Make a Conclusion About the null hypothesis. Since the p-value = :1 = or, we the null hypothesis. . We cannot conclude that the mean sales of McDonald's restaurants in North lI'Zarolina differ from average McDonald's sales worldwide. 0 We conclude that the mean sales of McDonald's restaurants in North Carolina differ from average McDonald's sales worldwide. A mayor running for re-election claims that during his term, average municipal taxes have fallen by $275. A conscientious statistician wants to test this claim. She surveys 39 of her neighbors and finds that their taxes decreased (in dollars) as follows: 259, 272, 278, 263, 256, 269, 291, 255, 275, 290, 307, 252, 279, 292, 291, 291, 314, 260, 263, 283, 278, 271, 286, 260, 253, 288, 292, 262, 290, 307, 308, 277, 269, 304, 297, 279, 287, 280, 244 The statistician assumes a population standard deviation of $17. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. 275 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 normally distributed | with distribution mean and distribution standard deviation 2.7223 Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P( xv ? v P(ZY ? v