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In: Statistics and Probability

For the following scenarios calculate the appropriate test statistic and make a decision based on the...

For the following scenarios calculate the appropriate test statistic and make a decision based on the provided decision rule. Be sure to explain what your decision means in the context of the problem.

a. The owner of a heating and air company would like to know whether there is a difference in the mean number of service calls made per day by two employees. To test this he conducts a hypothesis test at the .05 significance level with the following hypotheses:

H0: µA = µB

H1: µA ≠ µB

A random sample of 45 days for employee A shows he made an average of 19.3 calls per day. For a sample of 35 days, employee B made an average of 17.2 calls per day. Assume the population standard deviation for employee A is 2.3 calls and for employee B is 3.0 calls.

i. Test Statistic:

ii. What is your conclusion if the critical values for a two tail test are -1.96 and 1.96?

b. The manufacturer of a tire claims that the mean mileage the tire can be driven before the tread wears out is 65,000 miles. Assume the mileage wear follows the normal distribution and the standard deviation of the distribution is 5,400 miles. A truck company buys 50 tires and finds that the mean mileage for its trucks is 63,000 miles. Conduct a hypothesis test to determine if the company should believe the manufacturer’s claim at a .05 significance level

i. Test Statistic:

ii. What is your conclusion if the critical value for a left tail test is -1.645

Solutions

Expert Solution

To test,

H0: µA = µB

H1: µA ≠ µB

and are the true population mean values of numbers of service calls made per day by two employees A and B.

orchestra answered 2 years ago
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