Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.250 in a random sample of 56 at bats. For a random sample of 25 at bats since changing his training techniques, his batting average is 0.440. Determine if there is sufficient evidence to say that his batting average has improved at the 0.02
level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training be Population 2.

a. State the null and alternative hypotheses for the test. Fill in the blank below.
b. Compute the value of the test statistic. Round your answer to two decimal places.
c. Make the decision and state the conclusion in terms of the original question.

Audrey is training for her first marathon, and she wants to know if there is a significant difference between the true mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 55 randomly selected people who train in groups and finds that they run a mean of 46.9 miles per week. Assume that the population standard deviation for the group runners is known to be 5.2 miles per week. She also interviews a random sample of 45 people who train on their own and finds that they run a mean of 49.9 miles per week. Assume that the population standard deviation for people who run by themselves is 5.7
miles per week.

Find the P
-value for the hypothesis test. Round your answer to four decimal places.
b. Is there sufficient evidence to conclude that there is a significant difference between the true mean number of miles run each week by group runners and individual runners who are training for marathons? Test the claim at the 0.01 level of significance.

Adele and Jessica live in different states and disagree about who has the higher electric bills. To settle their disagreement, the girls decide to sample electric bills in their area for the month of July and perform a hypothesis test. The electric company in Adele’s state reports that a random sample of 51 monthly residential electric bills has a mean of $87.63. Assume that the population standard deviation in Adele's state is known to be $22.98. For a random sample of 35 monthly residential electric bills in Jessica's state, the mean is $84.22. Assume that the population standard deviation in Jessica's state is $21.45. Is there evidence at the 0.01
level to say that the mean monthly residential electric bill is higher for Adele’s state than for Jessica’s state?

Find the P
-value for the hypothesis test. Round your answer to four decimal places.
b. Is there sufficient evidence to conclude that the mean monthly residential electric bill is higher for Adele's state than for Jessica's state? Test the claim at the 0.01 level of significance.

An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 199 brakes using Compound 1 yields an average brake life of 47,673 miles. A sample of 157 brakes using Compound 2 yields an average brake life of 48,245 miles. Assume the standard deviation of brake life is known to be 3815 miles for brakes made with Compound 1 and 1538 miles for brakes made with Compound 2. Determine the 80%

confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

a. Find the critical value that should be used in constructing the confidence interval.
b. Construct the 80% confidence interval. Round your answers to the nearest whole number.

Eddie Clauer sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 11 sales receipts for mail order sales results in a mean sale amount of $93.90 with a standard deviation of $16.25. A random sample of 15 sales receipts for internet sales results in a mean sale amount of $86.60 with a standard deviation of $21.25. Using this data, find the 98%

confidence interval for the true mean difference between the mean amount of mail order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.

Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
b. Find the standard error of the sampling distribution to be used in constructing the confidence interval. Round your answer to two decimal places.
c. Construct the 98% confidence interval. Round your answers to two decimal places.