Question

a guidance counselor selected random samples of 25 ninth graders, 25 tenth graders, 25 eleventh graders, and 25 twelfth graders from her large high school. she asked each student whether they have a job. the results are displayed in the tables. observed counts: employed? yes: 9th - 3, 10th - 17, 11th - 15, 12th - 19; no: 9th - 22, 10th - 8, 11th - 10, 12th - 6. expected counts: employed? yes: 9th - 12.75, 10th - 12.75, 11th - 12.75, 12th - 12.75; no: 9th - 12.25, 10th - 12.25, 11th - 12.25, 12th - 12.25. she decides to test these hypotheses: ( h_0 ): there is no difference in the distribution of job status for all 9th, 10th, 11th, and 12th graders at this. for which categories were there more students observed than expected? there were more 9th graders than expected who did not have a job, and there were more 10th, 11th, and 12th graders than expected who did have a job. there were more 9th and 10th graders than expected who did not have a job, and there were more 11th and 12th graders than expected who did have a job. there were more 9th, 10th, and 11th graders than expected who did not have a job, and there were more 12th graders than expected who did have a job. there were more 11th and 12th graders than expected who did not have a job, and there were more 9th and 10th graders than expected who did have a job.

Explanation:

Step1: Compare observed and expected counts for each grade - job status combination

For 9th graders:
Observed "No" = 22, Expected "No" = 12.75. So, \(22>12.75\) (more 9th - "No" than expected).
Observed "Yes" = 3, Expected "Yes" = 12.25. So, \(3 < 12.25\)
For 10th graders:
Observed "No" = 11, Expected "No" = 12.75. So, \(11<12.75\)
Observed "Yes" = 17, Expected "Yes" = 12.25. So, \(17>12.25\)
For 11th graders:
Observed "No" = 10, Expected "No" = 12.75. So, \(10<12.75\)
Observed "Yes" = 15, Expected "Yes" = 12.25. So, \(15>12.25\)
For 12th graders:
Observed "No" = 6, Expected "No" = 12.75. So, \(6<12.75\)
Observed "Yes" = 19, Expected "Yes" = 12.25. So, \(19>12.25\)

Answer:

There were more 9th graders than expected who did not have a job, and there were more 10th, 11th, and 12th graders than expected who did have a job.