Question

The nonprofit group Public Agenda conducted telephone interviews with a stratified sample of parents of high school children. There were 202 black parent, 202 Hispanic parents, and 201 white parents. ONe question asked was, “Are the high schools in your state doing an excellent, good, fair, or poor job, or you don’t know enough to say?” Here are the survey results:

	Black	Hispanic	White	Total
Excellent	12	34	22	68
Good	69	55	81	205
Fair	75	61	60	196
Poor	24	24	24	72
Don't know	22	28	14	64
Total	202	202	201	605

(a) Give a 95% confidence interval for the proportion of families who think that the high schools are doing a “poor” job.

(b) You are interested in determining if the ratings of the schools differ among the sets of parents. Would you use a Chi-Square test of Independence or Homogeneity? Justify your answer.

(c) Use Crunchit to perform the Chi-Square test of significance. Report your findings.

Please show all work! Thank You!!

Answer 1

a)

Let ? = .05 and
?0:?ℎ? ????????????? ?? ??????? ??? ?ℎ? ???? ?? ???ℎ ????? ?? ???????
??:?ℎ? ????????????? ?? ??????? ??? ??? ?ℎ? ???? ?? ???ℎ ????? ?? ??????

Chi-Squared Test for Homogeneity of Populations

All participants were selected randomly and we’ll assume there are more than 6050 parents. All expected counts are greater than or equal to 5.

Do: ? 2 = 22.42 p-value = .004 with df= 8

c) Because the p-value = .004 < ? = .05, reject ?0.

Evidence suggests the distributions of opinion are not the same in each group of parents.

b)Homogeneity