PROBLEM 2 A parent advisory board for a certain university was concerned about t

Question

PROBLEM 2 A parent advisory board for a certain university was concerned about the effect of part-time jobs on the academic achievement of students attending the university. To obtain some information, the advisory board surveyed a simple random sample of 200 of the more than 20,000 students attending the university. Each student reported the average number of hours spent working part-time each week and his or her perception of the effect of part-time work on academic achievement. The data in the table below summarize the students' responses by average number of hours worked per week (less than 1 11 to 20, more than 20) and perception of the effect of part-time work on academic achievement (positive, no effect, negative) Average Time Spent on Part-Time Jobs Than 11 11 to 20 Hours More Than 20 Hours per Week Hours per Week per Week 21 Perception of the Effect of Part- Time Work on Academic No Effect Positive Effect tive Effect 18 A chi-square test was used to determine if there is an association between the effect of part-time work on academic achievement and the average number of hours per week that students work. Computer output that resulted from performing this test is shown below CHI-SQUARE TEST Expected counts are printed below observed counts 11 11-20 20 Total 35 16975 11200 6.825 No effect 32 105 15 50.925 33.600 20.475 23 29.100 9.200 700 Total 97 64 9 200 Chi-Sq 13.938, DF 4, P.Value 0.007 (a) State the and alternative hypotheses for this test (b) Discuss whether the conditions for a chi-square inference procedure are met for tese data. (c) Given the results from the chi-square test, what should the advisory board conclude? (d) Based on your conclusion in part (c), which type of error (Type I or Type II) might the advisory board have made Describe this error in the context of the question.

Explanation / Answer

a)

H0: The average time spent on part-time jobs are independent of the academic achievement

H1: The average time spent on part-time jobs are not independent of the academic achievement

b)

The chi-square tries to infer of the two variables are independent of each other. Here, it seems to have been satisfied

c)

p-value is less than 0.05. Hence, reject the null hypothesis. Thus, we conclude that the average time spent on part-time jobs are not independent of the academic achievement

d)

Here, we have rejected the null hypothesis. Hence, the type of error that could have been made would be type 1 error (incorrect rejection of a true null hypothesis).

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