A social psychologist hypothesized that a factor in juvenile delinquency was the presence or absence of a strong father-figure in the home. He examined the folders of 100 inmates in the federal reformatory and found that only 50 of these young men grew up with a strong father-figure in the home. He also examined the records of 100 randomly selected male college students and found that 70 of them had strong father-figures in their boyhood homes. Use the chi square method to test the psychologist’s hypothesis.
A labor official predicted that the following percentages of makes of cars would be seen passing a picket line at an automobile plant where a strike was in progress.
General Motors Ford Chrysler Foreign Brand

38% 28% 24% 10%

The following numbers of cars were counted. Analyze the data and write a conclusion about the official’s prediction.

General Motors Ford Chrysler Foreign Brand

114 72 75 41

On a test of independence between alcoholism and early toilet training, a clinical researcher found a c2 = 6.48. With df = 1 and a = .05, write a conclusion about the relationship between the two variables.
A mathematical learning theory predicted the percentages of nine different outcomes. The data were gathered, producing a c2 = 6.79 was found. Interpret the results in terms of the adequacy of the theory.
A 6 x 8 test of independence produced a chi square of 10.42. Write a conclusion about the inde- pendence of the two variables under consideration.
In an activity wheel, experimental animals were either isolated or put together and maintained on a restricted feeding schedule. After 25 days, the animals were either alive with stabilized weights or they were dead. Test for the independence of these two conditions with a c2 test. Use an a = .01.
Isolated Together

Alive 9 8

Dead 1 12

In a 3 x 5 test of independence, a c2 = 10.61 was calculated. Write a conclusion.
A theoretical model predicted the percentage of responses among six categories of response. On a test each person was counted in one of the six possible categories. A c2 = 12.10 was calculated. Write a conclusion about the theory.
At a busy street corner in a large city, right at the morning rush hour, a psychologist counted the number of people waiting for the light to change. A confederate dressed as a homeless man crossed the street against the light. The psychologist counted the number of people who followed him. When the next group collected to wait for the light to change, another confederate, dressed as a well-to-do businessman, crossed the street against the light, and the psychologist counted the number of people who followed him. Analyze the data.
Followed Did Not Follow

Homeless Man 3 15

Businessman 8 7

What can the psychologist say about the influence of appearance on whether or not a person takes risks?

10. a. Children were asked if they brushed their teeth regularly and, if so, with what brand of toothpaste. Children with dental caries (cavities) were identified. A statistician collected the records of children who brushed regularly and divided them into four categories of toothpaste. Brand A-185 records; Brand B – 210; Brand C – 150; and all others, 105. Each of these four sets was then divided into children who had caries and those who did not. The results were: A, 38 with caries, 147 without; B, 45 with caries, 165 without; C, 32 with caries, 118 without; others, 30 with caries, 75 without. Analyze the data and write a conclusion.

b. Suppose that of the 325 children who reported they didn’t brush regularly, 40% had caries. Use this fact and the data in 10a to determine if brushing is related to dental health.

Sample Solution