# Statistics: Hypothesis Tests

See the attached file for the proper symbols and formatting.

Part I T/F & Multiple Choice

1. An estimator is consistent if, as the sample size decreases, the value of the estimator approaches the value of the parameter estimated. ____ T/F

2. For a specific confidence interval, the larger the sample size, the smaller the maximum error of estimate will be. _____ T/F

3. When we reject the null hypothesis, we are certain that the null hypothesis is false. ___ T/F

4. The alternative hypothesis, sometimes referred to as the research hypothesis, is supported by using the sample evidence to contradict the null hypothesis. ___ T/F

5.  is the measure of the area under the curve of the standard score that lies in the rejection region for the null hypothesis. ___ T/F

6. Rejection of a null hypothesis that is false is a Type II error. ____ T/F

7. The maximum error of estimate is controlled by three factors: level of confidence, sample size, and standard deviation. ____ T/F

8. You are constructing a 95% confidence interval using the information: n = 50, = 54.3, s = 2.1 and E = 0.65. What is the value of the middle of the interval?

A. 2.1

B. 54.3

C. 50

D. 0.95

9. Which of the following would be the correct hypotheses for testing the claim that the mean life of a battery for a cellular phone (while the phone is left on) is at least 24 hours?

A. H0:   24 and Ha:  < 24

B. H0:  = 24 and Ha:   24

C. H0:   24 vs. Ha:  > 24

D. H0:  < 24 vs. Ha:   24

10. Which of the following would be the alternative hypothesis in testing the claim that the mean distance students commute to campus is no less than 8.2 miles?

A. Ha:   8.2

B. Ha:  > 8.2

C. Ha:  < 8.2

D. Ha:   8.2

Part II. Short Answers & Computational Questions

1. A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 175 was taken, and the mean amount spent was $250. Assuming a standard deviation equal to $45, find the 95% confidence interval for , the mean for all such families.

2. What sample size would be needed to estimate the population mean to within one-third standard deviation with 95% confidence?

3. A 95% confidence interval estimate for a population mean was computed to be (63.4 to 68.2). Determine the mean of the sample, which was used to determine the interval estimate.

4. In testing the hypothesis, H0:   31.5 and Ha:  < 31.5, using the p-value approach, a p-value of 0.0409 was obtained. If  = 8.7, find the sample mean which produced this p-value given that the sample of size n = 50 was randomly selected.

5. To test the null hypothesis that the average lifetime for a particular brand of bulb is 725 hours versus the alternative that the average lifetime is different from 725 hours, a sample of 100 bulbs is used. If the standard deviation is 50 hours and  is equal to 0.01, what values for will result in rejection of the null hypothesis.

6. Describe the action that would result in a type I error and a type II error if each of the following null hypotheses were tested.

a. H0: There is no waste in US Defense Department spending

b. H0: This fast-food menu is not low fat

7. By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 5.1 seconds.

a. How many measurements should be made in order to be 95% certain that the maximum error of estimation will not exceed 1.5 seconds?

b. What sample size is required for a maximum error of 2.5 seconds?

8. Determine the critical region and critical values for z that would be used to test the null hypothesis at the given level of significance, as described in each of the following:

a. H0:   51 and Ha:  > 51,  = 0.10

b. H0:   28 and Ha:  < 28,  = 0.01

c. H0:  = 93 and Ha:   93,  = 0.05

#### Solution Summary

Several questions on hypothesis tests, rejection region, Type 1 and 2 error, and confidence intervals are solved in this solution, which is given in Word format.