1.

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 36 of her neighbors and finds that their taxes decreased (in dollars) as follows: 257, 246, 261, 276, 244, 286, 310, 275, 288, 273, 255, 254, 316, 283, 278, 247, 251, 283, 244, 304, 255, 284, 266, 272, 283, 300, 274, 257, 308, 259, 272, 290, 303, 293, 257, 258 The statistician assumes a population standard deviation of $19. 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? Think about your answer to this step yourself; this step is not graded.

2.

The mean age when smokers first start is 13 years old with a population standard deviationof 1.9 years. A researcher thinks that smoking age has significantly changed since the invention of ENDSelectronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. Thesample of 32 smokers found that their mean starting age was 12 years old. Do the data support the claim at the 1% significance level?

What are the correct hypotheses?

H₀: Select an answer s s x p p ? < = > _________ years H₁: Select an answer s x p p s ? < = > _________ years

Based on the hypotheses, find the following:

Test Statistic z = ________ (Give answer to at least 4 decimal places) Critical Values =_________ (Give answer to at least 4 decimal places)

Based on the above we choose to Select an answer Fail to reject the null hypothesis Reject the null hypothesis Accept the null hypothesis ________

The correct summary would be: Select an answer__________ There is enough evidence to reject the claim There is not enough evidence to support the claim There is not enough evidence to reject the claim There is enough evidence to support the claim that the claim that the mean age smokers first start is different than 13.