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# Important information about Hypothesis Testing of Mean & Population proportion

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1. You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes.

From past experience, you can assume that the population standard deviation is 6 minutes. A sample of 36 orders using the new delivery process yields a sample of 22.4 minutes.

a) At the 0.05 level of significance, use the five-step p-value approach

2. In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service. During a period of one month, a random sample of 27 approved policies is selected, and the total processing time, in days, is recorded (as stored in the insurance.xls file):

73 19 16 64 28 28 31 90 60 56 31 56 22 18
45 48 17 17 17 91 92 63 50 51 69 16 17

a) In the past, the mean processing time was 45 days. At the 0.05 level of significance, is there evidence that the mean processing time has changed from 45 days?

3. Late payment of medical claims can add to the cost of health care. An article reported that for one insurance company, 85.1% of the claims were paid in full when first submitted. Suppose that the insurance company developed a new payment system in an effort to increase this percentage. A sample of 200 claims were paid in full when first submitted.

a) At the 0.05 level of significance, is there evidence that the proportion of claims processed under this new system is higher than the article reported for the previous system?

4. Suppose you saw an email that stated that the mean age of employees in your company is less than 40 years and that more than 50% of the employees are female. You decide to take a sample of employees and test the claim. Assume the Cumba database represents a random sample of 100 employees. Using the "Hypothesis Tests One Sample" file and a .05 significance level:

?Using the age data only, test whether the mean age is less than 40.
?Using the gender data only, test whether more than 50% of the employees are female.

Be sure to state your actual hypothesis, your decision to reject the null or not, and your conclusion plainly.