1. Testing: H0:=36H0:=36 H1:36H1:36 Your sample consists of 28 values, with a sample mean of 37.7. Suppose the population standard deviation is known to be 3.5. a) Calculate the value of the test statistic, rounded to 2 decimal places. z=z= b) At =0.03=0.03, the rejection region is

• z<-1.88orz>1.88z<-1.88orz>1.88
• z>2.17z>2.17
• z>1.88z>1.88
• z<-2.17orz>2.17z<-2.17orz>2.17
• z<-2.17z<-2.17
• z<-1.88z<-1.88

c) The decision is to

• Fail to reject the null hypothesis
• Accept the null hypothesis
• Accept the alternative hypotheis
• Reject the null hypothesis

d) Suppose you mistakenly rejected the null hypothesis in this problem, what type of error is that?

• Type I
• Type II

2. A mayor running for re-election claims that during his term, average municipal taxes have fallen by $250. A conscientious statistician wants to test this claim. She surveys 39 of her neighbors and finds that their taxes decreased (in dollars) as follows: 294, 328, 192, 250, 207, 279, 223, 192, 204, 287, 306, 219, 265, 260, 296, 230, 256, 276, 243, 338, 273, 253, 227, 294, 240, 206, 257, 192, 263, 197, 214, 231, 186, 281, 239, 238, 213, 289, 287 The statistician assumes a population standard deviation of $48. 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(? p' x ? )=P()=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?

3. The mean age when smokers first start is 13 years old with a population standard deviationof 1.8 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 34 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 p p s x s ? > = < years H₁: Select an answer p p s s x ? = > < 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 Reject the null hypothesis Accept the null hypothesis Fail to reject the null hypothesis

The correct summary would be: _______Select an answer :a.There is not enough evidence to reject the claim b. There is enough evidence to reject the claim c. There is enough evidence to support the claim d. There is not enough evidence to support the claim _________that the claim that the mean age smokers first start is different than 13.