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**ECON 2100 PROBLEM SET 10**

- From Mathematics, Statistics

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**ECON 2100**

**problem set 10**

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**Textbook questions**

Chapter 9: 1, 3, 45, 70, 71, 76, 77.

1.

Nan Compos-Mentis, a technical consultant, claims that she can increase average hourly productivity for the fabricators at Stryker Manufacturing by more than 10 units per worker. To support her claim, Nan plans to select a sample of workers, provide the workers in the sample with special training, and then use results from the sample in a hypothesis test designed to establish whether the training has had the desired effect. What null and alternative hypotheses would you recommend here?

3. In recent years the average time it takes audit teams from Trimble and Martin to complete a company audit has been 55.8 hours. In monitoring the performance of one of these audit teams recently, reviewers found that the average time for a random sample of team audits differed by nearly 6 hours from the company average. If you were to use the sample average in a hypothesis test to determine if this team's average performance is different from the overall company average, what null and alternative hypotheses would you recommend?

* *45. Suppose you are testing the following hypotheses:

H0:μ ≤ 1500

Ha:μ > 1500

Sample size is 25. The sample mean is 1545 and the sample standard deviation is 75. The significance level is .05. Assume that the values in the population are normally distributed.

1.Compute the sample test statistic, tstat.

2. With the help of a statistical calculator or a statistical software package, determine the appropriate p-value here and use it to conduct the test. (If you are using Excel, use the statistical function T.DIST.RT to produce the appropriate p-value.)

3. Based on your work in parts a and b, should you reject the null hypothesis? Explain

70. Your friend Fred claims that his average gym workout time is at least 150 minutes per day. You pick a random sample of 10 days and observe that on the days in the sample, Fred's average workout time was 136 minutes. The standard deviation of workout times in the sample was 28 minutes. You plan to use the sample results to test Fred's claim. Assume that Fred's workout times are normally distributed.

Set up an appropriate hypothesis test to test Fred's claim. Use a significance level of 5%. Should Fred's claim be rejected? Explain.

71. Refer to Exercise 70. Suppose sample size was 50 days rather than 10 days. Show the proper hypothesis test and report your conclusion.* *

76. You have set up a hypothesis test to determine if the plywood sheets being produced by your mill meet company standards. For each large batch of sheets, you select a sample of six sheets and count the number of surface flaws in each. You then compute the average number of flaws in the sample and use the sample result to test the following hypotheses:

H0: μ ≤ 3.5 (The average number of flaws in the large batch of plywood sheets is 3.5 or less.)

Ha: μ > 3.5 (The average number of flaws in the batch of plywood sheets is greater than 3.5.)

Suppose a particular sample of six sheets yields the following data:

Use a significance level of .05. Assume that the population distribution of flaws in a sheet is normal. Determine the p-value for the sample mean here and use it to decide whether you can reject the null hypothesis. (If you are using Excel, use the statistical function T.DIST.RT.)

77. From a recent production run of compact fluorescent (CF) bulbs, you select a random sample of 10 bulbs. Using an accelerated bulb life simulation, you find that the average life for the bulbs in the sample is 2440 hours, with a sample standard deviation of 60 hours. Use these sample results to test, at the 5% significance level, the null hypothesis that the average life for the full population—the entire production run—of bulbs is precisely 2500 hours, no more and no less. Report your conclusion and explain.

**Statistical investigation**

These questions again use data from a survey of Albers students conducted in Fall 2014, regarding their housing situation. The data are found in the file “housing survey data fall 2014.”

Nationwide, the average household size in 2010 was determined to be 2.58 people (www.census.gov). You would like to conduct a hypothesis test at a 5% significance level to determine whether there is evidence that the household size for Albers students differs from the national average.

a. State the null and alternative hypothesis for the test.

b. Calculate the appropriate test statistic (t-stat) for the test.

c. What is the critical value for the test?

d. Do you reject, or not reject, the null hypothesis? Explain your decision based on the critical value.

e. Find the *p-value* for the hypothesis test (use Excel’s T.DIST.2T function).

f. Using the *p-value, *explain your decision regarding the null hypothesis (reject/not reject).

g. Summarize your conclusion in a sentence or two: what does the test show about household size?

**Everyday statistics**

Please read the article “When Whites Get a Free Pass,” linked here and posted along with the assignment.

a. Briefly describe the study: what strategy was used to test for racial discrimination?

b. The fourth paragraph of the article includes the sentence, “the study uncovered substantial, statistically significant race discrimination.” What does ‘”statistically significant” mean here?

c. In the sentence, “the study uncovered substantial, statistically significant race discrimination,” what evidence is provided to show that the racial discrimination was substantial (socially or economically significant)?

d. This study is in the tradition of “audit testing,” in which randomized trials are used to test for discrimination. What is particularly original about this “audit test”?

**ECON 2100 PROBLEM SET 10**

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- Submitted On 13 Jun, 2017 08:45:27

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