Business Statistics - Stats Project

Hypothesis Tests of the Mean

Part 1: Par, Inc.

Par., Inc., is a major manufacturer of golf equipment. Management believes that Par’s market share could increase with the introduction of a cut-resistant, longer-lasting golf ball. Therefore, the research group at Par has been investigating a new golf ball coating designed to resist cuts and provide a more durable ball. The tests with the coating have been promising. It is important however that the new coating does not reduce the driving distance of the ball.

One of the researchers voiced concern about the effect of the new coating on driving distances. Par needs to ensure the new cut-resistant ball can offer driving distances comparable to those of the current-model golf ball. The average driving distance for the current model is known to be 270 yards. To compare the driving distances for the two balls, 40 balls of the new model balls were subjected to distance tests. The testing was performed with a mechanical hitting machine so that any differences between the mean distance for the new model could be attributed to a difference in the two models. The results of the tests, with the distances measured to the nearest yard, follow. The complete data set can be found on D2L as an accompanying file called GOLF1.MTW.

Data :

Assignment :

Prepare a managerial report that addresses the following issues below. In particular, you must decide whether you stand behind the conclusions derived by the statistical analysis or whether more testing (and therefore additional expense) is recommended. The target audience for this report is your boss, a senior marketing manager at Par who has a basic understanding of business statistics. Your supervisor will be displeased if your conclusions are in error: You supported the new model based on limited evidence or you recommended further testing and the company incurred expenses that turn out to be unnecessary upon further review of the original data. Of course, if the report is exemplary you may expect it to be circulated more widely in the company to your credit.

1. Formulate and present the rationale for a one-tailed hypothesis test with a 95% confidence level that Par could use to evaluate the driving distances of the new golf balls.
2. Use Minitab to analyze the data to provide the hypothesis testing conclusions. In particular, state both the statistical decision and the proper interpretation of the statistical decision in the context of this analysis. Include the following information in your report: What is the ρ-value for your test? What is your recommendation for Par, Inc. based on this sample?
3. Use Minitab to provide descriptive statistical summaries of the data for the new model. (Consider Minitab Project 1 for insights on the appropriate descriptive statistics to provide.) You may use Excel to construct suitable tables for inclusion in your final report.
4. Use Minitab to construct the 95% confidence interval for the population mean for the new model.
5. Provide your ow n personal recommendation to clearly answer the following question: Do you see a need for larger samples and more testing with the golf balls? In your answer, discuss whether or not a larger sample could potentially affect the results. Could your conclusion change? Explain why or why not based on your understanding of statistics.

Part 2: Wentworth Medical Center

As part of a long-term study of individuals 65 years or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression. A sample of the data collected follows; higher test scores indicate higher levels of depression. The complete data set can be found on D2L as an accompanying file called MEDICAL1.MTW.

A second part of the study considered the relationship between the geographic location and depression for individuals 65 years of age or older who had a chronic health condition such as arthritis, hypertension, and/or heart ailment. A sample of 60 individuals with such conditions was identified. Again, 20 were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. A sample of the levels of depression recorded for this study follow. The complete data set can be found on D2L as an accompanying file called MEDICAL2.MTW.

Sample Data :

Assignment :

Prepare a statistical analysis report that addresses the following issues below. In particular, you must clearly state the major conclusions derived by the statistical analysis of each study’s results. The target audience for this report is the physician who undertook the two studies, who you may assume has a basic understanding of business statistics.

1. Use Minitab to provide descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores from the two studies? Are there differences between the studies that appear significant? Are there differences between the states that appear significant within each study?
2. Use Minitab to conduct a comparison analysis on the Medical1 data set. For the data on each state (Florida, New York, and North Carolina) from Medical1, test the hypothesis that the population mean is different from a score of 7.0 for each state. Use a 90% confidence level for your hypothesis tests. Clearly s tate the hypotheses being tested in all three cases for each data set. You will perform three hypothesis tests in all, one for each state. What are your conclusions? Include and interpret properly formatted evidence from the Minitab output to support your conclusions.
3. Use Minitab to conduct a comparison analysis on the Medical2 data set. For the data on each state (Florida, New York, and North Carolina) from Medical2, test the hypothesis that the population mean is different from a score of 15.0 for each state. Use a 90% confidence level for your hypothesis tests. Clearly state the hypotheses being tested in all three cases for each data set. You will perform three hypothesis tests in all, one for each state. What are your conclusions? Include and interpret properly formatted evidence from the Minitab output to support your conclusions.

Price: $33.12

Solution: The downloadable solution consists of 13 pages, 2012 words and 8 charts.
Deliverable: Word Document