# Hypothesis Testing Problems and Confidence Intervals

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 mu, 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: mu >= 31.5 and Ha: mu < 31.5, using the p-value approach, a p-value of 0.0409 was obtained. If sigma = 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 alpha is equal to 0.01, what values for Xbar 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: mu =< 51 and Ha: mu > 51, alpha = 0.10
b. H0: mu >= 28 and Ha: mu < 28, alpha = 0.01
c. H0: mu = 93 and Ha: mu =/= 93, alpha = 0.05

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