Please show all work.

Please show all work and include whether chart or calculator was used. show all work MAT 308 Chapters 8 & 10.1& 10.2 (135 Total Points) Name:__________________________ 1. Find zα/2 for the following levels of α (5 points each): a. α=.66 b. α=.30 c. α=.06 2. Find zα/2 for the following confidence levels (5 points each): a. 80% b. 70% c. 89% 3. Construct a 95% confidence interval and find the margin of error for the mean of a normal population if a random sample of size 60 from the population yields a sample mean of 90 and the population has a standard deviation of 10(10 points). 4. Forty panels were exposed to various corrosive conditions to measure the protective ability of paint. The mean life for the samples was 112 hours. The life of the paint samples is assumed to be normally distributed with a population standard deviation of 25 hours. Find the 85% confidence interval and the margin of error for the mean life of the paint (10 points). 5. Suppose you sample 19 baseball pitchers and find that they have an average pitching speed of 87 mph with a standard deviation of 0.98 mph. Find a 95% confidence interval and margin of error for the average pitching speed of all pitchers (10 points). 6. Find tα/2, n-1 for two tails the following combinations of α and n (5 points each). a. α=.05, n=25 b. α=.20, n=3 c. α=.01, n=34 7. Travel agency claims that the average 5-day vacation will cost no more than $700 per person. A researcher believes that the average cost is higher and decides to test her theory with a hypothesis test. The conclusion of the hypothesis test is to fail to reject the null hypothesis. What does this conclusion say about the researcher’s claim (5 points)? 8. The failure rate of an algebra course is no more than 35%. Researchers decide to reject the null hypothesis. The actual failure rate is 34%. Did the researchers make an error? If yes, what type (5 points)? 9. Construct a 98% confidence interval for the mean of a normal population assuming that the values listed below comprise a random sample taken from the population. The population standard deviation is unknown (15 points). Must Include Sample Mean and Standard Deviation 22 30 15 9 2 4 27 16 29 10. The wait mean time of a national chain of banks is at most 3.00 minutes. A manager believe that the wait time is more than 3.00 minutes. She tracks the wait times of 55 people. The mean time was 3.35 minutes. Assuming the population standard deviation is 1.5 minutes, is there sufficient evidence to say that the mean wait time is longer than 3.00 minutes with a 98% level of confidence (10 points)? 11. A worldwide credit card company wondered whether giving frequent flyer miles for every purchase would increase card usage, which has a current mean of $3,200 per year. They gave free miles to a random sample of 350 credit card customers and found the sample mean to be $3,254. Assume the population standard deviation is σ=$139 (15 points). α level: 0.05 Find: Ho: Ha: Calculate the test statistic: P-value: Reject or fail to reject Ho State the conclusion. 12. According to the Health Department in one state, the mean weight for men is 185.7 pounds. A local doctor has designed a plan to reduce the weight of men. He takes a random sample in his town of 52 men, and he finds that they have a mean weight 181.3 pounds. Assuming that the population standard deviation is 3.5 pounds, is there sufficient evidence at 0.05 level of significance to say that the mean weight of men in this town is lower than the state weight of 185.7 (10 points)?