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Hypothesis Testing on Multiple Scenarios

Problem 1
Consider the Mission Valley Power Company (MVP), which has over 6000 customers. In response to a request from the Michigan Public Utilities Commission, MVP needs to estimate the average kilowatts of electricity used by customers on April 1. The only way to get this number is to select a random sample of customers and take a meter reading after 5 p.m. on March 31 and again after 5 p.m. on April 1. The commission has specified that any estimate presented in the utility's report must have a margin of error not to exceed ± 30 kilowatts. MVP has estimated that the standard deviation of kilowatts used is approximately 200. Using this information, find the sample size required in parts A - C.

a) A desired level of 90% confidence for the population mean kilowatt usage.
b) A desired level of 95% confidence for the population mean kilowatt usage.
c) A desired level of 99% confidence for the population mean kilowatt usage.
d) When the desired margin of error is fixed, what happens to the sample size as the confidence level is increased?

Would you recommend a 99% level of confidence to be used in this case? Why or why not? Explain.

Problem 2
The Quick-Lube Company operates a chain of oil change outlets in several states. Quick-Lube recommends that customers have their oil changed every 3 months or 3000 miles, whichever comes first. When the customer comes in for service, the date and mileage are recorded and a computer program tracks the customers so that when the 3 month time frame is near a reminder card is sent to the customer. A new reminder card was designed in hopes of getting more repeat business from the customers. A sample of 100 customers received the new reminder card and 62 customers returned to have their oil changed within a month after the card was mailed.

a) At 90% confidence, what is the margin of error associated with the estimated proportion of customers who return for a Quick-Lube oil change within a month after receiving the new card?
b) What is the 90% confidence interval for the proportion of customers who return for a Quick-Lube oil change within a month after receiving the new card?
c) How large a sample should be taken if the desired margin of error is ± .04 with 95% confidence?

Problem 3

The Elgin Heart Institute performs many open heart surgeries at its 10 facilities in the United States. Recently, research physicians at Elgin have developed a new heart bypass surgery procedure that they believe will reduce the average recovery time for patients. Records indicate that the average recovery rate for the standard procedure is 42 days with a standard deviation of 5 days. To determine if the new procedure actually results in a lower average recovery time, the procedure was performed on a sample of 36 patients. The average recovery time was found to be 40.2 days for the 36 patients. Test the Elgin research physicians' claim using a .05 level of significance.

Problem 4

The Wilson Sales Company is a contract provider of telephone solicitations. In this capacity, the sales staff makes "cold calls" to people in various target markets in an attempt to sell a product or service for Wilson's clients. The more sales that are made, the more revenue Wilson receives. The new management at Wilson feels that calls made between 6 and 7 p.m. are more effective for selling items than calls made between 7:30 and 8:30 p.m.
The company made 200 calls at random between 6 and 7 p.m. and another 200 calls between 7:30 and 8:30 p.m. and recorded the number of sales. There were 14 sales made during the 6-7 p.m. calls and 9 sales made during the 7:30-8:30 p.m. calls. Use this information to test the new management's claim at the .10 level of significance.

Problem 5

Benton Industries manufactures carpets and draperies in the Atlanta area. Benton Industries pays market wages, provides competitive benefits, and offers other attractive options for employees in an effort to reduce turnover and create a satisfied workforce. At a recent meeting, several supervisors complained that employee absenteeism was becoming a problem. In response to these complaints, the human resource manager conducted a study involving a random sample of 500 employees with the results shown in the table below.

One aspect of this study was to determine whether there is a relationship between absenteeism and marital status. Absenteeism during the past year was broken down into three levels.

Level 1 is No Absences, Level 2 is 1-5 Absences, and Level 3 is Over 5 Absences
Marital status was divided into four categories. 1-Single 2-Married 3-Divorced and 4-Widowed

Test to see if there is a relationship between absenteeism and marital status using a .025 level of significance.
Absenteeism Rate
Marital Status Zero Absences 1-5 Absences Over 5 Absences
Single 88 82 30
Married 56 58 36
Divorced 44 40 16
Widowed 12 20 18

Solution Summary

This solution shows step-by-step calculations to determine multiple statistical analyses such as sample size, margin of error, and confidence interval. It also conducts hypothesis testing by stating the decision rule, calculating the test statistic, comparing it to the p-value and making a decision to accept or reject the null hypothesis.