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Homework 3

Due date: Nov. 4, 2014.

Note: all hypothesis testing problems should specify the null and alternative hypotheses and report the p-value of the data.

  1. A large corporation has a plant that has started a pilot program to give stock options for its assembly line workers as part of their benefits package. The corporation would like to determine if the mean quality score for this plant exceeds the current average quality measure of 75. A random sample of 20 production units is selected from this plant and the quality scores for these units are obtained. The mean score for these units is 78.2 with a s.d. of 10.3.

  2. A company is said to be out of compliance if more than 10% of all invoices contain errors, and it is considered to be seriously out of compliance if more than 15% of all invoices contain errors. Suppose an auditor randomly selects a sample of 1250 invoices and found that 200 contained errors.

  3. A random sample of 48 students took an SAT preparation course prior to taking the SAT. The sample mean of their quantitative SAT scores was 560 with a s.d. of 80, and the sample mean of their verbal SAT scores was 520 with a s.d. of 110.

  4. A fabrication plant has just completed a contract to supply memory chips to a computer manufacturer that requires the defective rate of these chips to be no more than 8%. The plant has just installed new equipment to produce these chips. An initial production run of 400 chips will be obtained and one of three actions will be taken depending on the results of this run. If it is shown that more than 8% of the chips are defective, then the equipment will be recalibrated to reduce the defective rate; if it is shown that less than 8% of chips are defective, then cheaper raw material will be used to reduce costs; otherwise, the equipment will be unchanged and production will begin. Suppose that among the initial production of 400 chips it was found that 28 chips were defective.

  5. A large corporation would like to determine if employee job satisfaction will improve if it includes profit sharing based on quality scores for its factory workers. To answer this question, a pilot program was begun at one of its factories. A random sample of 30 workers from this factory was selected and, separately, a random sample of 30 workers was selected from another of its factories that did not implement this program. Prior to the start of the program each worker in these samples was given a test of job satisfaction as part of their normal review process. This test was then administered to the same employees six months after the start of the new program. Use 5% level of significance for the following questions. The data is contained in the file

  6. A soft drink company would like to increase its market share of diet soft drinks among 18-25 year old females with a new ad campaign targeting this population by placing ads at web sites these women are likely to visit. A random sample of 250 females in this age bracket who drink these products is selected to participate in a study to estimate the proportion of such women who visit these sites, as well as how often they visit them in a week. The file
    contains the number of times each woman in this sample visited the sites during a typical week.

next up previous
Next: Example R scripts Up: Homework and Project Assignments Previous: Homework 2
Larry Ammann