Please show all work.

1) The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:

11 8 8 10 11

9 9 14 8 5

Find a 95% confidence interval for the population standard deviation .

Test the given claim. Use the P-value method or the traditional method as indicated. Identify the null hypothesis,

alternative hypothesis, test statistic, critical value(s) or P-value, conclusion about the null hypothesis, and final

conclusion that addresses the original claim.

Please show work.

2. A simple random sample of 15-year old boys from one city is obtained and their

weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights

come from a population with a mean equal to 149 lb. Assume that the standard deviation of the weights of all

15-year old boys in the city is known to be 16.2 lb. Use the traditional method of testing hypotheses.

147 138 162 151 134 189 157 144 175 127 164

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic,

P-value, critical value(s), and state the final conclusion.

Please show work.

3. Test the claim that the mean lifetime of car engines of a particular type is greater

than 220,000 miles. Sample data are summarized as n = 23, x = 226,450 miles, and s = 11,500 miles. Use a

significance level of = 0.01.