1. Testing: H0:31.8H0 H1:<31.8H1 Your sample consists of 46 values, with a sample mean of 30.3. Suppose the population standard deviation is known to be 3.47. a) Calculate the value of the test statistic, rounded to 2 decimal places. z=__? b) At =0.04=0.04, the rejection region is?

• z<-2.05
• z<-2.05orz>2.05
• z<-1.75orz>1.75z
• z>2.05
• z<-1.75
• z>1.75

c) The decision is to

• Accept the null hypothesis
• Fail to reject 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 $150. A conscientious statistician wants to test this claim. He surveys 38 of his neighbors and finds that their taxes decreased (in dollars) as follows: 176, 76, 196, 169, 131, 84, 197, 144, 178, 157, 164, 150, 160, 144, 142, 117, 200, 147, 180, 77, 129, 125, 173, 175, 164, 157, 196, 111, 96, 124, 74, 174, 144, 148, 111, 130, 164, 182 The statistician assumes a population standard deviation of $40. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. p or ?__ 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 or 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' or x ? or ?)=_______? P=(z or t ? or ? )=________? 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.

3. The average McDonald's restaurant generates $3.4 million in sales each year with a standard deviation of 0.5. Miguel wants to know if the average sales generated by McDonald's restaurants in Kansas is different than the worldwide average. He surveys 27 restaurants in Kansas and finds the following data (in millions of dollars): 3.4, 3.1, 3.7, 3.8, 3.3, 2.7, 2.4, 2.7, 2.4, 3.2, 4, 2.9, 3.3, 2.8, 2.4, 2.8, 2.7, 3.6, 2.9, 2.8, 3.3, 2.3, 2.5, 3.8, 3.2, 3.4, 3 Perform a hypothesis test using a 4% level of significance. Step 1: State the null and alternative hypotheses. H0: p or ? < > = ? Ha: p or ? < > = ? (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 or t-distributed? with distribution mean_____? and distribution standard deviation _____? Step 3: Find the p-value of the point estimate. P(p' or x ? or ? ____)P( z or t? or )______? p-value=_____? Step 4: Make a Conclusion About the null hypothesis. Since the pp-value=? < or ________? =, we Select an answer: reject or do not reject ?the null hypothesis.

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

4. 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 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 (s p s x p ) (< = > ) ____ years H₁: Select an answer( x p s s p ) ?( > = <) ____ 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 Fail to reject the null, hypothesis Accept the null hypothesis ?

The correct summary would be:

There is not enough evidence to support the claim?

There is enough evidence to reject 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.