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I don't understand Chi-squaring?

The student population at the state college consists of 55% females and 45% males

a. The college theater department recently staged a production of a modern musical. A researcher recorded the gender of each student entering the theater and found a total of 385 females and 215 males. Is the gender distribution for the theater goers significantly different from the distribution for the general college? Test at the .05 level of significance.



Report the chi-square value; do you reject the null hypothesis?



b. The same researcher also recorded the gender of each student watching a men’s basketball game in the college gym and found a total of 83 females and 97 males. Is the gender distribution for basketball fans significantly different from the distribution for the general college? Test at the .05 level of significance.



Report the chi-square value; do you reject the null hypothesis?





Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that the younger drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtains information about registered drivers from the department of motor vehicles and selects a sample of n=300 accident reports from the police department. The motor vehicle department reports the percentage of registered drivers in each age category as follows: 16% are under the age 20; 28% are 20 to 29 years old; and 56% are 30 or older. The number of accident reports for each age group is as follows:



Under Age Age 30

Age 20 20-29 or older

68 92 140

68 92 140



a. Calculate and report the chi-square test statistic.

b. Do you reject or fail to reject the null hypothesis?





Gender differences in dream content are well documented. Suppose a researcher studies aggression content in the dreams of men and women. Each participant reports his or her most recent dream. Then each dream is judged by a panel of experts to have low, medium, or high aggression content. The observed frequentcies are shown in the following matrix:



Aggression Content



Low Medium High

Female 18 4 2

Gender

Male 4 17 15


Is there a relationship between gender and the aggression content of dreams? Test with a=.01.

a. Calculate and report the chi-square test statistic.

b. Do you reject or fail to reject the null hypothesis?





Research indicates that people who volunteer to participate in research studies tend to have higher intelligence than nonvolunteers. To test this phenomenon, a researcher obtains a sample of 200 high school students. The students are given a description of a psychological research study and asked whether they would volunteer to participate. The researcher also obtains an IQ score for each student and classifies the students into high, medium, and low IQ groups. Do the following data indicate a significant relationship between IQ and volunteering? Test at the .05 level of significance.



IQ

High Medium Low

Volunteers 43 73 34 150

Non Volunteers 7 27 16 50


50 100 50



a. Calculate and report the chi-square test statistic.

b. Do you reject or fail to reject the null hypothesis?



Although the phenomenon is not well understood, it appears that people born during the winter months are slightly more likely to develop schizophrenia than people born at other times. The following hypothetical data represent a sample of 50 individuals diagnosed with schizophrenia and a sample of 50 individuals diagnosed with schizophrenia and a sample of 100 people with no psychotic diagnosis. Each individual is also classified according to season in which he or she was born. Do the data indicate a significant relationship between schizophrenia and the season of birth? Test at the .05 level of significance.

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