# Important information about Hypothesis Testing of Mean & Population proportion

See attached files.

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.

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#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis of mean and population proportion. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

Standard Error, Confidence Interval and Hypothesis Testing

I need some help with these hypothesis testing and standard error questions:

1. The mean of a normal probability distribution is 60; the standard deviation is 5.

(a) About what percent of the observations lie between 55 and 65?

(b) About what percent of the observations lie between 50 and 70?

(c) About what percent of the observations lie between 45 and 75?

2. A normal population has a mean of 12.2 and a standard deviation of 2.5.

1. Compute the z value associated with 14.3.

2. What proportion of the population is between 12.2 and 14.3?

3. What proportion of the population is less than 10.0?

3. The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of $70,000 and a standard deviation of $20,000. A loan application is received this morning. What is the probability:

1. The amount requested is $80,000 or more?

2. 2. The amount requested is between $65,000 and $80,000?

3. The amount requested is $65,000 or more?

4. Jon Molnar will graduate from Carolina Forest High School this year. He took the American College Test (ACT) for college admission and received a score of 30. The high school principal informed him that only 2 percent of the students taking the exam receive a higher score. The mean score for all students taking the exam is 18.3. Jon's friends Karrie and George also took the test but were not given any information by the principal other than their scores. Karrie scored 25 and George 18. On the basis of this information, what were Karrie's and George's percentile ranks? Assume that the distribution of scores follows the normal distribution.

5. A population consists of the following five values: 2, 2, 4, 4, and 8.

1. List all samples of size 2, and compute the mean of each sample.

2. Compute the mean of the distribution of sample means and the population mean. Compare the two values.

3. Compare the dispersion in the population with that of the sample means.

6. A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation 0.5 pounds. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than 0.2 pounds?

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