Assignment:
Q1: You want to find out if there is a gender effect on a person's attitude regarding abortion. Your survey 140 subjects and find that of the 88 females questioned; 59 feel that abortion should be legal and 29 do not. Of the 52 males questioned, 15 feel that it should be legal and 37 do not. What can you conclude about the effect of a person's gender on the abortion issue?
A) What are the dependent and independent variables?
B) What are your null and alternate hypotheses (no formulas) ?
C) What is your decision?
Q2: You are interested in the effect of reward VS punishment on your communications with your employees. To test the effect you setup a study, which analyzes how this effects communication. You divide employees into groups and test their knowledge of recent communications. The results follow:
A) What are the dependent and independent variables ?
B) What are your null and alternate hypotheses, no formulas ?
C) How many levels were in the treatment?
D) How many subjects were in the study?
E) What is your decision?
Q3: A diaper company is considering 3 different filler materials for their disposable diapers. Eight diapers were tested with each of the 3 filler materials and 24 toddlers were randomly given a diaper to wear. As the child played, fluid was injected into the diaper every 10 minutes until the product failed (leaked). The amount of fluid (in grams) at the time of failure was recorded for each diaper. The data are shown below:
| Material 1 |
Material 2 |
Material 3 |
| 791 |
809 |
828 |
| 789 |
818 |
814 |
| 796 |
803 |
855 |
| 802 |
781 |
844 |
| 810 |
813 |
847 |
| 790 |
808 |
848 |
| 800 |
805 |
836 |
| 790 |
811 |
873 |
a) What is the response variable and what is the factor?
b) How many levels of the factor are being studied?
c) Is there any difference in the average amount of fluid the diaper can hold using the 3 different filler materials? If so, which ones are different?
d) What is your recommendation to the company and why?
Q4: A large company sells software. The company had received complaints that the disks provided by the company failed to work properly after extended use. The company has decided to investigate the complaint. Data are collected on the time to failure for disks from their current supplier and two alternative suppliers. The data are shown below:
| Current Supplier |
Alternative 1 Supplier |
Alternative 2 Supplier |
| 486 |
489 |
508 |
| 490 |
489 |
510 |
| 491 |
491 |
517 |
| 491 |
492 |
506 |
| 494 |
492 |
515 |
| 494 |
492 |
520 |
| 496 |
492 |
503 |
| 498 |
493 |
507 |
| 498 |
493 |
515 |
| 502 |
494 |
503 |
| 504 |
495 |
507 |
| 505 |
496 |
515 |
| 506 |
497 |
509 |
| 507 |
497 |
518 |
| 508 |
497 |
495 |
| 510 |
498 |
499 |
| 514 |
499 |
510 |
| 515 |
502 |
503 |
| 527 |
503 |
533 |
| 498 |
505 |
517 |
a) What is the response variable and what is the factor?
b) How many levels of the factor are being studied?
c) Is there any difference in the average time to failure of the disks from the 3 different suppliers? If so, which ones are different?
d) What is your recommendation to the company and why?
Q5: Grading homework is a real problem. It takes an enormous amount of time and many students do not do a very good job or copy answers from other students or the back of the book. A teacher of elementary statistics decided to conduct a study to determine what effect grading homework had on her students' exam scores. She taught 3 sections of Elementary Statistics and randomly assigned each class one of the three conditions : 1) no homework given 2) homework given but not collected, and 3) homework given, collected, and graded. After the first exam, she collected the data (exam scores). They are shown below:
| No Homework |
Homework, Not Collected |
Homework, Collected |
| 69 |
73 |
83 |
| 69 |
63 |
97 |
| 92 |
68 |
72 |
| 84 |
79 |
79 |
| 79 |
57 |
84 |
| 84 |
68 |
76 |
| 76 |
72 |
91 |
| 63 |
74 |
76 |
| 76 |
49 |
83 |
| 82 |
84 |
88 |
| 89 |
79 |
91 |
| 72 |
71 |
96 |
| 72 |
80 |
68 |
| 65 |
74 |
99 |
| 73 |
71 |
89 |
| 47 |
63 |
80 |
| 92 |
88 |
79 |
| 71 |
83 |
91 |
| 83 |
89 |
83 |
| 81 |
82 |
83 |
| 92 |
69 |
76 |
| 80 |
92 |
90 |
| 64 |
79 |
79 |
| 72 |
81 |
67 |
| 84 |
76 |
86 |
| 79 |
81 |
86 |
| 74 |
81 |
82 |
| 81 |
75 |
84 |
a) What are the response variable and what is thefactor?
b) How many levels of the factor are being studied?
c) Is there any difference in the average exam scores using the 3 different approaches to homework? If so, which ones are different?
d) What is your recommendation to the teacher and why?
Q6: The sports industry is a large and competative market. A manufacturer of golf balls is considering 4 new ball designs. A sample of 36 balls from each of the 4 models is tested and the distance the balls cary (in yards) is recorded. The balls are hit by a machine. The data is shown below:
|
M1 Model |
M2 Model |
M3 Model |
M4 Model |
| 1 |
257 |
256 |
244 |
250 |
| 2 |
255 |
255 |
243 |
255 |
| 3 |
256 |
258 |
241 |
251 |
| 4 |
255 |
257 |
243 |
249 |
| 5 |
255 |
257 |
240 |
250 |
| 6 |
256 |
257 |
249 |
251 |
| 7 |
255 |
258 |
244 |
251 |
| 8 |
258 |
258 |
249 |
248 |
| 9 |
252 |
256 |
248 |
247 |
| 10 |
256 |
258 |
243 |
253 |
| 11 |
253 |
258 |
242 |
250 |
| 12 |
254 |
256 |
245 |
255 |
| 13 |
260 |
259 |
253 |
250 |
| 14 |
258 |
255 |
250 |
256 |
| 15 |
258 |
259 |
251 |
260 |
| 16 |
257 |
257 |
249 |
259 |
| 17 |
259 |
256 |
249 |
252 |
| 18 |
257 |
255 |
249 |
253 |
| 19 |
255 |
255 |
255 |
257 |
| 20 |
256 |
257 |
249 |
255 |
| 21 |
259 |
260 |
251 |
251 |
| 22 |
261 |
255 |
250 |
255 |
| 23 |
260 |
261 |
248 |
253 |
| 24 |
257 |
262 |
250 |
256 |
| 25 |
260 |
258 |
258 |
262 |
| 26 |
262 |
260 |
258 |
258 |
| 27 |
258 |
260 |
257 |
263 |
| 28 |
260 |
256 |
258 |
259 |
| 29 |
258 |
255 |
254 |
256 |
| 30 |
258 |
256 |
256 |
261 |
| 31 |
258 |
257 |
255 |
258 |
| 32 |
256 |
251 |
254 |
258 |
| 33 |
260 |
253 |
255 |
256 |
| 34 |
260 |
254 |
260 |
263 |
| 35 |
261 |
254 |
254 |
264 |
| 36 |
257 |
255 |
253 |
257 |
a) What is the response variable and what is the factor?
b) How many levels of the factor are being studied?
c) Is there any difference in the average distance the ball carries?
d) What is your recommendation to the golf manufacturer and why?
Q7: As a part of a survey on the use of Office Suites Software, the company doing the polling wanted to know whether its population was uniformly distributed over the following age distribution: 25,25 to 44, 45 and up. The company looked at the data it had collected so far and found the following distribution:
| Age Group |
Number of Respondents |
| Under 25 |
73 |
|
| 25 to 44 |
61 |
|
| 45 and up |
66 |
|
| Total |
200 |
|
a) Based on the data, do you think that the respondents are uniformly distributed over the age categories?
b) Set up the hypotheses to test whether the data are uniformly distributed over the age categories.
c) Find the expected frequency distributed and perform the chi-square goodness of fit test.
d) At the 0.05 level of significance, would you say that the respondents were uniformly distributed over the age groups?