# EBook Problems Hypothesis L Mean

## EBook Problems Set - Testing a Claim about a Mean: Large Samples

### Problem 1

Hong is a pharmacist studying the effect of an anti-depressant drug. She organizes a simple random sample of 100 patients, and then collect their anxiety test scores before and after administering the anti-depressant drug. Hong wants to estimate the mean difference between the pre-drug and post-drug test scores. How should she proceed?

(a) She should compute a confidence interval or conduct a hypothesis test
(b) She should calculate the z or the t statistics
(c) She should compute the correlation between the two samples
(d) Not enough information to tell

### Problem 2

A utility company serves 50,000 households. As part of a survey of customer attitudes, they take a simple random sample of 750 of these households. The average number of television sets in the sample households turns out to be 1.86, and the standard deviation in the sample is 0.80. What sample size would be necessary for the standard error of the sample mean to be 0.02?

(a) 5,000
(b) 1,600
(c) 10,000
(d) 1,000

### Problem 3

Statistics show that the average level of a mother's education for a city of 300,000 people is 14 years with a standard deviation of 1.5 years. A major state university is located in this town. The administrators in this university think that the average level of a mother's education for the freshmen who are admitted to this school is higher than 14 years. The average education level of mothers for a random sample of 100 freshmen who were admitted to this university within the last two years was 14.7 years.

We want to test the null at the level of alpha = 0.001. What is the best answer?

(a) We reject the alternative and believe that the level of a mother's education for university freshmen is not higher than the overall population average.
(b) We reject the null at 0.001 and conclude that the average level of a mother's education is higher for university freshmen.
(c) We fail to reject the null and conclude that the level of a mother's education for university freshmen is not higher than the overall population average.
(d) In order to be certain about the conclusion we reach, a larger sample size is needed to increase the power of the test and the margin of error.

### Problem 4

A class of 50 eighth-graders took a standardized reading test. Their scores had a mean of 107.5 and a standard deviation of 10.5. The national mean score on the test is 100. The probability of observing an x-bar as large or larger than 100 if the null hypothesis is true is

(a) Equal to 0.05
(b) Larger than 0.05
(c) Smaller than 0.05