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# PART I. HYPOTHESIS TESTING Problem 1: 35 points Conduct a one-tailed hypothesis test given the information below.

PART I. HYPOTHESIS TESTING

Problem 1: 35 points
Conduct a one-tailed hypothesis test given the information below.

The waiting time for patients at a local walk-in health clinic follows a normal distribution with a mean of 15 minutes and a population standard deviation of 5 minutes. The quality-assurance department sampled 50 patients and found that the mean waiting time was 14.25 minutes. At the 0.025 significance level, decide if the sample data support the claim that the mean waiting time is less than 15 minutes. State the null and alternative hypothesis. State the critical value. Draw a diagram. Provide the computation of the test statistic. State your decision in terms of the null hypothesis.

Problem 2: 35 points
Conduct a two-sample test of means
A study by a bank compared the average savings of customers who were depositors for three years or less with those who had been depositors for more than three years. The results of a sample are:

To test that the two groups of customers have equal savings rates, what is the critical value of z using α = 0.05?

Problem 3. 50 points
Conduct a two-tailed hypothesis test given the information below.

producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next.

A. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but assumed equal. What is the critical t value at the 1% level of significance? Note: The table in the exam is for one-tail tests—be sure to double the percentage for a two-tail test.

B. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, what is the decision?

Problem 4. 50 points
Conduct a two-tailed hypothesis test given the information below.

Assume that the population standard deviations are equal for income mutual funds and growth mutual funds. Use the following sample data to test whether there is a difference in the mean yields of the two funds at the 0.05 level of significance.

Income Growth
Sample Size 35 40
Sample Mean 900 875
Sample Standard Dev 35 45

What is the null hypothesis?

What is the computed value of the test statistic t?

What is the p value for this test statistic?

What decision is made about the null hypothesis using an α = 0.05?

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