- In a recent poll, incumbent city council candidate Iam N. deMoney was favored by 725 of 1500 registered voters. Find the 95% confidence interval for the true proportion of registered voters favoring deMoney. The same poll revealed that 710 of the 1500 favor challenger Anita Job. (The other voters polled had no favorite or mentioned another name.) Find her 95% confidence interval. Do you feel confident in predicting the outcome of this election? Explain.
- A manufacturer of replacement bulbs for LCD projectors claims a 1000 hour average life time for the bulbs. This is important, since the bulbs sell for around $300 each. Concerned that the claim may not be valid because of a recently discovered problem in the manufacturing process, the company decides to test it. Twelve bulbs are randomly selected from a production run, each is burned until it fails, and its lifetime recorded. Here are the 12 lifetimes, in hours.
988 972 1024 978 986 959 965 1015 1010 1007 979 1001
What do these 12 lifetimes suggest about the manufacturer’s claim? Be specific about assumptions, hypotheses being tested, test statistic used, and the critical region for your test. Interpret the results of your test in regard to the claim of the bulb manufacturer. (You may do this test by hand or get SPSS to do it for you. If you use SPSS, please provide the output it produces along with your interpretation of the results.) Note that you have not been asked for nor should you consider a confidence interval in this problem.
- The faculty of a university mathematics department is concerned about the performance of students in the introductory calculus offered by the department and required of all science and engineering majors. Historically, class averages on the final exam have been about 75, a passing grade but indicative that students may not be learning the material as well as they need to in order to go on to the next course. The chair would like to raise the average to at least 80. The department decides to implement a tutoring program in which each section of the course has assigned to it an advanced student who has done very well in the course previously. That student attends the section assigned and is available for student consultation 10 hours each week outside of class. A random sample of 50 students from the first semester of the program is selected and the final exam score for each student in the sample is recorded. The sample of scores is provided below.
78 75 74 73 70 75 70 71 77 78
74 77 81 76 78 72 73 73 75 77
72 82 80 74 72 77 77 73 79 75
74 80 78 76 79 81 75 71 74 78
75 71 75 77 72 74 77 75 77 78
What do these 50 scores suggest about the chair’s concern? Be specific about assumptions, hypotheses being tested, test statistic used, and the critical region for your test. Interpret the results of your test in regard to the concerns of the chair. (You may do this test by hand or get SPSS to do it for you. If you use SPSS, please provide the output it produces along with your interpretation of the results.) As in problem 2, you need not consider any confidence intervals.