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Statistical Analysis and Hypothesis Testing Questions

Question 1 - Out-of-Pocket Medical Expenses for Prescription Drugs

Question 1:
The Center on Budget and Policy Priorities reported that average out-of-pocket medical expenses for prescription drugs for privately insured adults with incomes over 200% of the poverty level was $173 in 2002. Suppose an investigation was conducted in 2009 to determine whether the increased availability of generic drugs, Internet prescription drug purchases, and cost controls have reduced out-of-pocket drug expenses. The investigation randomly sampled 196 privately insured adults with incomes over 200% of the poverty level, and the respondents’ 2009 out-of-pocket medical expenses for prescription drugs were recorded. These data are in the file Drug Expenses. Based on the sample data, can it be concluded that 2009 out-of-pocket prescription drug expenses are lower than the 2002 average reported by the Center on Budget and Policy Priorities? Use a level of significance of 0.01 to conduct the hypothesis test.
Question 2:
Hono Golf is a manufacturer of golf products in Taiwan and China. One of the golf accessories it produces at its plant in Tainan Hsing, Taiwan, is plastic golf tees. The injector molder produces golf tees that are designed to have an average height of 66 mm. To determine if this specification is met, random samples are taken from the production floor. One sample is contained in the file labeled THeight.
a. Determine if the process is not producing the tees to specification. Use a significance level of 0.05.
b. If the hypothesis test determines the specification is not being met, the production process will be shut down while causes and remedies are determined. At times this occurs even though the process is functioning to specification. What type of statistical error would this be?
Question 3:
Cell phones are becoming an integral part of our daily lives. Commissioned by Motorola, a new behavioral study took researchers to nine cities worldwide from New York to London. Using a combination of personal interviews, field studies, and observation, the study identified a variety of behaviors that demonstrate the dramatic impact cell phones are having on the way people interact. The study found cell phones give people a newfound personal power, enabling unprecedented mobility and allowing them to conduct their business on the go. Interesting enough, gender differences can be found in phone use.

Women see their cell phone as a means of expression and social communication, whereas males tend to use it as an interactive toy. A cell phone industry spokesman stated that half of all cell phones in use are registered to females.
a. State the appropriate null and alternative hypotheses for testing the industry claim.
b. Based on a random sample of cell phone owners shown in the data file called Cell Phone Survey, test the null hypothesis. (Use ? = 0.05.)
c. The study also wants to test which group gender spent money on their mobile phone. Conduct the statistical test at significance level 0.05. Discuss your finding.
Question 4:
Suppose a professional job-placement firm that monitors salaries in professional fields is interested in determining if the fluctuating price of oil and the outsourcing of computer-related jobs have had an effect on the starting salaries of chemical and electrical engineering graduates. Specifically, the job placement firm would like to know if the 2007 average starting salary for chemical engineering majors is higher than the 2007 average starting salary for electrical engineering majors. To conduct its test, the job placement firm has selected a random sample of 124 electrical engineering majors and 110 chemical engineering majors who graduated and received jobs in 2007. Each graduate was asked to report his or her starting salary. The results of the survey are contained in the file Starting Salaries. Conduct a hypothesis test to determine whether any differences between mean starting salary for 2007 graduates in chemical engineering with mean starting salary for 2007 graduates in electrical engineering. Conduct the test at the 0.05 level of significance. Be sure to test the normality assumption.

Question 2 - Height of Plastic Golf Tees

Question 5:
A treadmill manufacturer has developed a new machine with softer tread and better fans than its current model. The manufacturer believes these new features will enable runners to run for longer times than they can on its current machines. To determine whether the desired result is achieved, the manufacturer randomly sampled 35 runners. Each runner was measured for one week on the current machine and for one week on the new machine. The weekly total number of minutes for each runner on the two types of machines was collected. The results are contained in the file Treadmill. At the 0.02 level of significance, can the treadmill manufacturer conclude that the new machine has the desired result?
Question 6:
A business statistics instructor at State University has been experimenting with her testing procedure. This term, she has taken the approach of giving two tests over each section of material. The first test is a problem-oriented exam, in which students have to set up and solve applications problems. The exam is worth 50 points. The second test, given a day later, is a multiple-choice test, covering the concepts introduced in the section of the text covered by the exam. This exam is also worth 50 points. In one class of 15 students, the observed test scores over the first section of material in the course are contained in the file State University.
a. If the instructor is unwilling to make the assumptions for the paired-sample t-test, what should she conclude based on these data about the distribution of scores for the two tests if she tests at

a significance level of 0.05?
b. In the context of this problem, define a Type II error.
Question 7:
USA Today notes (Mary Beth Marklein, “College Gender Gap Widens: 57% Are Women”) that there are more men than women ages 18–24 in the United States—15 million versus 14.2 million. The male/female ratio in colleges today is 42.6/57.4. However, there is a discrepancy in the percentage of males’ dependent on their parents’ income. The file entitled Diversity contains the gender of undergrads (18–24) whose parents’ income is in two categories: (1) low income—less than $30,000, and (2) upper income—$70,000 or more.
a. Determine if the sample sizes are large enough so that the sampling distribution of the difference between the sample proportions of male undergraduates in the two income categories can be approximated by a normal distribution.
b. Perform a test of hypothesis to determine that the proportion of male undergraduates in the upper income category is more than 1% greater than that of the low-income category. Use a significance level of 0.01

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