# mathematics

1. Air Force Training Program Case Study
An Air Force introductory course in electronics uses a personalized system of instruction whereby each student views a videotaped lecture and then is given a programmed instruction text. The students work independently with the text until they have completed the training and passed a test. Of concern is the varying pace at which the students complete this portion of their training program. Some students are able to cover the programmed instruction text relatively quickly, whereas other students work much longer with the text and require additional time to complete the course. The fast students wait until the slow students complete the introductory course before the entire group proceeds together with other aspects of their training.
A proposed alternative system involves use of computer-assisted instruction. In this method, all students view the same videotaped lecture and then each is assigned to a computer terminal for further instruction. The computer guides the student, working independently, through the self-training portion of the course.
To compare the proposed and current methods of instruction, an entering class of 122 students was assigned randomly to one of the two methods. One group of 61 students used the current programmed-text method and the other group of 61 students used the proposed computer-assisted method. The time in hours was recorded for each student in the study. The following data are provided in the attached data set.

1. Use the methods of (Chapter 10 – Inference About Means and Proportions with Two Populations) to comment on any difference between the population means for the two methods. Discuss your findings.
1. Compute the standard deviation and variance for each training method. Conduct a hypothesis test about the equality of population variances for the two training methods. Discuss your findings.
1. What conclusion can you reach about any differences between the two methods? What is your recommendation? Explain.

Wentworth Medical Center

2. As part of a long-term study of individuals 65 years of age 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. The data collected follow; higher test scores indicate higher levels of depression. These data are contained in the file Wentworth1.
A second part of the study considered the relationship between geographic location and depression for individuals 65 year 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. The levels of depression recorded for this study follow. These data are contained in the file named Wentworth2.
1. Use descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores?
 Wentworth 1 Wentworth 2 Florida New York North Carolina Florida New York North Carolina Mean 5.55 8.15 7.2 14.5 15.4 13.9 Standard Error 0.4783 0.4429 0.5921 0.7090 0.8808 0.5472 Median 6 8 7.5 14.5 14.5 14 Mode 7 8 8 17 14 12 Standard Deviation 2.1392 1.9808 2.6477 3.1706 3.9390 2.4473 Sample Variance 4.5763 3.9237 7.0105 10.0526 15.5158 5.9895 Kurtosis -1.0622 0.8889 -0.7423 -0.3408 0.1289 -1.0067 Skewness -0.2736 1.1692 0.0439 0.2807 0.6784 0.2241 Range 7 7 9 12 15 8 Minimum 2 6 3 9 9 10 Maximum 9 13 12 21 24 18 Sum 111 163 144 290 308 278 Count 20 20 20 20 20 20

2. Use analysis of variance on both data sets. State the hypotheses being tested in each case. What are your conclusions?

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