Assignment 5, Fall 2000

STATISTICS 403 - Assignment 5

Due Thursday, October 19, 2000

Hotpoint has a standard material for use in insulating the ovens of stoves that they manufacture. They decide to explore the use of a different material that is cheaper to purchase but may not have the same degree of insulating power. Below are the times it takes for ovens to cool down to 350 F after being heated to 400 F and the heating element turned off.
```
Standard 
Material, X   13.9   14.2   14.9   15.1   15.3   15.7   16.1   17.2
Cheaper 
Material, Y   12.9   13.7   14.0   14.1   14.4   14.7   14.8   15.4 
```
- (a) Use the two sample t-test (assuming equal variances) to see if the mean cool down time for the standard material is greater than that of the cheaper material. Use alpha=0.05.
- (b) Use the Mann-Whitney-Wilcoxon test to see if the standard material maintains the heat longer than the cheaper material. Use alpha=0.05 and Table H.
- (c) Do the tests give consistent results? How do the P-values compare?
- (d) Give a point estimate and a 95% confidence interval for the difference in mean cool down times for the two materials, again assume equal variances.
- (e) Give a point estimate and a 95% confidence interval for the difference in median cool down times for the two materials. You must display the 64 differences, Delta_ij = X_i - Y_j and use Table H.
- (f) Do these confidence intervals give consistent results?
- (g) Write a summary of your findings. You should direct this summary to the vice president in charge of purchasing. In the summary you should comment on what changing to the cheaper material would cost in terms of insulating power (ability to hold heat longer).
Data is collected on the amount of time spent by students at the ISU Recreation Facility. Thirty students, 15 males and 15 females are observed. The elapsed time (minutes) spent during one visit to the area that has the aerobic fitness devices, weight machines and free weights is recorded for each student.
```
               Males, X                Females, Y

          52  75  74  68  93       63  32  86  53  49
          77  41  87  72  53       73  39  56  45  67
          84  65  66  69  62       49  51  65  54  56
```
- (a) Use the Mann-Whitney-Wilcoxon test statistic to test for a difference between males and females in terms of the time they spend at the ISU Recreation Facility. Use a normal approximation. Be sure to give the mean and standard deviation of U. Since there are so few tied ranks you do not have to correct for these in this problem.
- (b) The value 86 for a female time is a misrecording of the actual value of 36. Change this value and repeat part (a).
Fifty Middle-Aged Men and fifty Young Adult Men were rated on physical flexibility. The scale went from 1, least flexible, to 10, most flexible. The table below shows a summary of these ratings. For example, no young adult men had a flexibility rating of 1, while 1 middle-aged man received this rating.
```
  Physical    Young    Middle
Flexibility   Adult     Aged
   Rating      Men       Men
------------------------------
      1         0         1
      2         0         2
      3         3         3
      4         4         4
      5         6         7
      6         7         9
      7         9        11
      8        10         8
      9         7         5
     10         4         0
------------------------------
```
- (a) Construct a graphical display of the data that compares the distribution of physical flexibility scores for young adult men to those of middle aged men. How do the two distributions compare?
- (b) Would a two-sample t-test be appropriate for comparing the mean flexibility scores for the two groups of men? Briefly explain.
- (c) Use Tukey's quick test to test to see if young adult men tend to be more physically flexible than middle aged men.
- (d) Use the Mann-Whitney-Wilcoxon test to see if young adult men tend to be more physically flexible than middle aged men. Use a normal approximation and correction for tied ranks. Be sure to give the mean and standard deviation of U.