R Exercise #4

Requirements

1. Complete the assignment in R and submit your R file. In your R file, please
2. clearly indicate which question you are answering with your R code.
3. You may find the following resources helpful:

• Elementary Statistics with R (http://www.r-tutor.com/elementary- statistics).
• oMostRrelatedproblemsfollowthisRtutorial.
• oInadditiontotheRTutorialvideoforbeginners(Seeblackboard),the
• section "R Introduction" will give you a starting point for learning R.
• https://www.youtube.com/watch?v=VGKz3Jkx-9I&t=326s(This video
• helps with joint frequency distribution, a.k.a. cross-tabulation or contingency table).

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Problem 9

A consumer research group is interested in testing an automobile manufacturer's claim that a new economy model will travel at least 25 miles per gallon of gasoline.

1. Provide a null and alternative hypothesis for the test.
2. Suppose a test on 25 cars of this model indicates an average of 24 mpg, with asamplestandard deviation of 3 mpg. Compute the value for the test statistic and the p-value.
3. Suppose the significance level is 5%. Compute the critical value for the test statistic. What conclusion should we draw for the test? Provide a practical interpretation for this conclusion.
4. Compute the critical value for the sample mean and determine the when we should reject H0and when we should accept H0.
5. Provide a practical interpretation of Type II error in this case.
6. Compute the probability of committing a Type II error (denoted as) if the actual mileage is 23 mpg as well as the power of the test.

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Problem 10

Par, Inc., is a major manufacturer of golf equipment. Management believes that Par's market share could be increased 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. One of the researchers voiced concern about the negative effect of the new coating on driving distances. Par would like the new cut-resistant ball to offer driving distances no worse than those of the current- model golf ball. To compare the driving distances for the two balls, 40 balls of both the new and current models were subjected to distance tests. The testing was performed with a mechanical hitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the two models. The results of the tests, with distances measured to the nearest yard, are in the file "Golf.csv". Let the current-model golf balls be population 1 and the new cut- resistant balls be population 2. Complete the following.

1. Formulate and present the rationale for a hypothesis test that Par could use to compare the driving distances of the current and new golf balls.
2. Provide descriptive statistical summaries of the data for each model; in particular, the sample mean, the sample standard deviation, and the sample size for each model.
3. Compute the standard error for your test.
4. Compute the degree of freedom for your test.
5. Compute the test statistic for your test.
6. Compute the p value for your test.

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1. Suppose the significance level is set at 5%. What is your conclusion? Provide a practical interpretation of your conclusion in this case.
2. Use the function t.test() in R to run the test directly to confirm your results above are correct.
3. What is the 95% confidence interval for the population mean driving distance of the current model?
4. What is the 95% confidence interval for the population mean driving distance of the new model?
5. What is the 95% confidence interval for the difference between the means of the two populations?

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