Instructions:
For each of the following questions, perform a hypothesis test. Make sure that you include each of the following if you want full credit:
1) Hypotheses
2) Type of test (two tailed, right tailed, or left tailed)
3) Test statistic
4) Alpha
5) P-value-with a picture
6) Critical value(s)-with a picture
7) Reject or not reject the null hypothesis
8) What that means for the problem-a sentence or two explaining which, if any, mean is higher
9) How can this information help the decision maker?
You can use Excel and/or do your calculations by hand to complete the assignment.
Question 1: from Essentials of Modern Business Statistics, 4th edition; Anderson, Sweeney and Williams Arnold Palmer and Tiger Woods are two of the best golfers to ever play the game. To show how these two golfers would compare if both were playing at the top of their game, the following sample data provide the results of 18 holes' scores during the PGA tournament competition. Palmer's scores are from his 1960 season, while Wood's scores are from his 1999 season. Use these sample results to test the hypothesis of no difference between the population mean 18-hole scores for the two golfers.
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Arnold Palmer
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Tiger
Woods
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n
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112
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84
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xbar
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69.95
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69.56
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Assume a population standard deviation of 3 for both golfers.
Perform a hypothesis test to determine if there is a difference between the two golfers' average scores. Use an alpha level of .10.
Question 2: from Data Analysis and Decision Making with Microsoft Excel, Second Edition; Albright, Winston and Zappe
Many companies are now installing exercise facilities at their plants. The goal is not only to provide a perk for their employees, but to make the employees more productive by getting them in better shape. Xerox Company installed exercise equipment on site a year ago. To check whether it is having a beneficial effect on employee productivity, the company has gathered data on a sample of 80 randomly chosen employees, all between the ages of 30 and 40 and all with similar job titles and duties. The company observed which of these employees use the exercise facility regularly. This group included 23 of the 80 employees in the sample. The other 57 employees were asked whether they exercise regularly elsewhere, and six of them replied they did. The remaining 51, who admitted to being nonexercisers, were then compared to the combined group of 29 exercisers.
The comparison was based on the employees' productivity over the year, as rated by their supervisors. Each rating was on a scale of 1 to 25, 25 being the best. The average score for exercisers was 17.5 with a sample standard deviation of 4.10. For those who don't exercise on a regular basis, the mean score was 14.3 and the sample standard deviation was 5.3. Do these data support the company's hypothesis that exercisers outperform nonexercisers on average? Use a significance level of .05.
Question 3: from Data Analysis and Decision Making with Microsoft Excel, Second Edition; Albright, Winston and Zappe
The ArmCo Company, a large manufacturer of automobile parts, has several plants in the USA. For years, ArmCo company has complained that their suggestions for improvements in the manufacturing process are ignored by upper management. In response, a manager at the Midwest plant decided to initiate some policies to respond to employee suggestions. No such initiatives were taken at the other ArmCo plants. As expected, there was a great deal of employee enthusiasm at the Midwest plant shortly after the new policies were implemented, but the question was whether life would revert to normal and the enthusiasm would dampen with time.
To check this, 100 randomly selected employees at the Midwest plant and 300 employees from other plants were asked to fill out a questionnaire 6 months after the implementation of the new policies at the Midwest plant.
Employees were instructed to respond to each item on the questionnaire by checking "yes" or "no". Two questions were on the questionnaire:
1. Management at this plant is generally responsive to employee suggestions for improvements
2. Management at this plant is more responsive to employee suggestions now than it used to be.
The responses are summarized below:
Question 1 Results:
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Midwest Plant
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Other
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Those who responded "Yes"
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39
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93
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Total number sampled
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100
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300
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Question 2 Results:
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Midwest Plant
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Other
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|
Those who responded "Yes"
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68
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159
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|
Total number sampled
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100
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300
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Does it appear that workers at the Midwest plant are more satisfied about management's response than workers elsewhere? Should ArmCo implement these policies in its other plants? Select your own alpha value.
Question 4:
Longston Enterprises operates businesses in the Minnesota area. Recently, the company was notified by the law firm representing several female employees that a lawsuit was going to be filed claiming that males were given preferential treatment when it came to pay raises by the company. Using the data file (on Canvas) Longston Enterprises, can it be proven at a .01 level of significance that the mean percentage raises granted to males is greater than that given to females? Assume that the population variances are about equal.
Question 5:
The Federal Reserve reported in its comprehensive Survey of Consumer Finances that the average income of families in the US declined from 2001 to 2004. This was the first decline since 1989-1992. A sample of incomes was taken in 2001 and repeated in 2004. After adjusting for inflation, the data that arise from these samples are given in a file titled Federal Reserve. Use a significance level of 0.05 to determine if the decline in incomes in 2004 is statistically significant.
Question 6: from Essentials of Modern Business Statistics, 4th edition; Anderson, Sweeney and Williams
Suppose employees at a manufacturing company can use two different methods to perform a production task. To maximize production output, the company wants to identify the method with the shorter population mean completion time. A simple random sample of 6 workers is selected. Each worker first uses one method and then uses the other method. The order of the two methods is assigned randomly to the workers. The results are in the table below:
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Worker
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Completion Time for Method 1 (in minutes)
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Completion Time for Method 2
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1
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6
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5.4
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2
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5
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5.2
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3
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7
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6.5
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4
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6.2
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5.9
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5
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6
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6
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6
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6.4
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5.8
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Using a significance level of 0.01, can we conclude that mean time of method 1 is different than the mean time of method 2?