EDUR 8131

Chi Square Exercise (answers provided below)

Instructions

Present results using the table format found in the notes entitled "Reporting Statistical Outcomes." Do not include SPSS output; present only results tables and written comments on results.

Results must be typed and due at beginning of class on the date listed on Course Index.

1. Is sex associated with the likelihood of stopping at a stop sign? To determine whether these two variables are related, a researcher observed, over a one-hour period, the behavior of drivers at an intersection in Statesboro. Do these data provide sufficient evidence, at the .05 level of significance, to indicate a relationship between sex and likelihood of stopping at a stop sign? Here are the results:

Males who stopped completely = 14 out of a total of 48 male drivers observed

Females who stopped completely = 15 out of a total of 37 female drivers observed

(Note that you can determine all four combinations of sex by stopping from the information provided, i.e., males who stopped completely, males who did not stop completely, etc.)

2. Employees of a firm that manufactures a product suspected of being associated with respiratory disorders were cross-classified by level of exposure to the product and whether or not they exhibited symptoms of respiratory disorders. The results are shown in the table below. Do these data provide sufficient evidence, at the .01 level of significance, to indicate a relationship between level of exposure and the presence of respiratory disorder symptoms?

 Exposure Level Symptom displayed No Exposure Limited Exposure High Exposure Yes 5 9 46 No 16 18 30

3. Preparation time and success in examination. The following table shows the number of students who passed or failed an examination, and the number of hours that these students dedicated to the study of topics covered in the exam. After the final exam, students were asked how much time they devoted for the preparation of the exam, and were classified into three groups (less than 5 hours, between 5 and 10 hours, and more than 10 hours). Following are the results.

Pass Fail
Less than 5 hours 11 15
5 to 10 hours 25 7
More than 10 hours 35 7
Total 71 29

Based on the information above, can you conclude that there is a statistically significant difference, at the .01 level, in success between the groups of students with different numbers of hours of preparation?

4. GSU claims that its racial distribution of students parallels the racial distribution of Georgia residents. In Georgia, the following percentages hold for 2000 population estimates:

Asian = 2.5%

Black = 27.4%

Hispanic/Latino = 6.3%

Other = 1.2%

White = 62.6%

GSU enrollment by Race

 Asian Black Hispanic Other White 257 3,754 214 286 11,193

Total Enrollment = 15,704

Does the racial distribution of enrolled students at GSU differ statistically from what would be expected based upon racial population of Georgia?

1. Is sex associated with the likelihood of stopping at a stop sign?

Stop sign behavior by sex

 Males Females Stopped 14 (29.16%) 15 (40.54%) Did Not Stop 34 (70.83%) 22 (59.46%)

χ2 = 1.20, df = 1, p > .05

The available data indicate that one's likelihood of stopping at a stop sign does not differ by sex of driver. Both males and females demonstrated similar patterns of stopping (or lack of stopping) completely at stop signs.

2. Do these data provide sufficient evidence, at the .01 level of significance, to indicate a relationship between level of exposure to the product and the presence of respiratory disorder symptoms?

Level of product exposure and respiratory disorder symptoms display.

 Exposure Level Symptom displayed No Exposure Limited Exposure High Exposure Yes 5 (23.80%) 9 (33.33%) 46 (60.53%) No 16 (76.20%) 18 (66.67%) 30 (39.47%)

χ2 = 12.04, df = 2, p < .01

Results of the statistical analysis reported above demonstrate a statistically significant difference in rates of displaying respiratory disorder symptoms across levels of product exposure. Only about 24% of those with no product exposure displayed respiratory disorder symptoms, about 33% with limited product exposure displayed symptoms, but just over 60% with high exposure to the product displayed respiratory disorder symptoms.

3. Preparation time and success in examination.

Hours Spent Studying and Testing Results

 Time Spent Studying Test Result Fewer than 5 hours 5 to 10 hours More than 10 hours Pass 11 (42.31%) 25 (78.13%) 35 (83.33%) Fail 15 (57.69%) 7 (21.87%) 7 (16.67%)

χ2 = 14.29, df = 2, p < .01

There is a statistically significant difference in passing rates among levels of hours spent studying. Students who spent 5 to 10 hours studying, or more than 10 hours studying, had passing rates of about 78% and 83% respectively. However, students with fewer than 5 hours studying demonstrated a passing rate of only 42%.

4. GSU enrollment and GA population racial distribution

There is a statistically significant difference in GSU racial enrollment patterns and the population racial distribution of Georgia residents statewide ( χ2 = 963.77, df = 4, p < .01). Generally speaking, it appears that Asian, Black, and Hispanic students are under-represented while White and "Other" students are over-represented.

NOTE: I incorrectly reported the chi-square in #4 as 96.77 by inadvertently omitting the 3 from 963.