15.2 During last year's budget crunch, several deserving employees of the Bureau of Procedures (BP) were denied promotions. This year, an unusual number of BP employees retired. The bureau chief suspects that the denial of promotions resulted in increased retirements. Of the 115 employees denied promotion, 32 retired. Of the 58 employees promoted, 9 retired. Present a contingency table, and analyze this information.
15.4 Auditors for the Military Airlift Command (MAC) are checking the arrival times of the three charter airlines they used in the Pacific last year. Branflake Airways flew 135 flights and was late 78 times. Flying Armadillo Airlines flew 94 flights and was late 35 times. Air Idaho flew 115 flights, with 51 late arrivals. Set up a contingency table, and analyze it for MAC.
16.4 Two scholars are locked in debate regarding the interpretation of the accompanying data. One insists that the relationship between the age of a child and the child's perception of the parents is very strong; the other argues that no relationship exists. Why do the two scholars reach different conclusions? Analyze the table and resolve the dilemma. Is there a relationship between the age of a child and the child's perception of the parents?
Age of Child (Years)
Child's Perception of Parents 5-15 16-27 28 and Older
Negative 11% 53% 23%
Neutral 18% 27% 59%
Positive 71% 20% 18%
Total 100% 100% 100%
16.6 The city parks commission has decided to redevelop a community park. Some members of the commission feel that refurbishment of existing park facilities is sufficient to meet the needs of the community; therefore, they advocate minimal redevelopment. Other members feel that such a small-scale project is pointless. They contend that improvement of the park will create greater public satisfaction with the park and thus will draw many more people than currently use it. An increase in patrons could exhaust existing facilities, thus necessitating further redevelopment. To resolve this disagreement, the commission hires a consultant to conduct a survey of community opinion. Among the questions asked are these: Do you regularly use the park? Do you consider park facilities satisfactory or unsatisfactory? From the cross-tabulation of these questions presented in the accompanying table, what should the consultant recommend to the commission?
Use Park Unsatisfactory Satisfactory Total
No 401 107 508
Yes 180 50 230
Total 581 157 738
Total 100% 100% 100%
17.2 The Department of Defense is concerned about the number of Harrier crashes. The Air Force argues that the crashes result because many of these planes are piloted by marines. The data for this claim are shown in the following table:
Result Marine Air Force Total
Crash 46 32 78
Did not crash 187 155 342
Total 233 187 420
When the number of flight hours of the pilot is controlled, the following pattern appears:
Pilot with Less Than 200 Hours Pilot with More Than 200 Hours
Result Marine Air Force Total Marine Air Force Total
Crash 36 26 62 10 6 16
Did not crash 62 51 113 125 104 229
Total 98 77 115 135 110 245
Analyze these tables and present your findings.
17.4 A researcher is conducting an experiment to determine support for the feminist movement. The experimental procedure consists of playing a tape recording of a meeting of a feminist organization for a group of subjects and then comparing their attitudes with those of a matched control group of subjects who are not exposed to the tape. At the conclusion of the experiment, the researcher is amazed to find that the tape recording apparently made no difference in attitude toward the feminist movement. Check this result in the following table:
Listened to Tape Recording
Attitude toward Feminist Movement
Not favorable 40 39
Favorable 40 41
The researcher then decides to take into account the sex of the subjects and obtains the following tables:
Listened to Tape Recording Listened to Tape Recording
Attitude toward Feminist Movement Attitude toward Feminist Movement ???? No Yes No Yes
Not favorable 21 24 Not favorable 19 15
Favorable 19 16 Favorable 21 25
Did the tape recording have an effect on attitude toward the feminist movement? Explain your answer.
The solution gives detailed steps on conducting the chi square test to check the independent of two variables by setting up a contingency table.
Chi Square test of a Contingency Table
In a chi-squared test of a contingency table, the value of the test statistic was =12.678, and the critical value at = 0.025 was 14.4494. Thus,
a. we fail to reject the null hypothesis at = 0.025
b. we reject the null hypothesis at = 0.025
c. we don't have enough evidence to accept or reject the null hypothesis at = 0.025
d. we should decreased the level of significance in order to reject the null hypothesis