Question

A television station wishes to study the relationship between viewership of its 11 p.m. news program and viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older). A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station’s 11 p.m. news is found for each sample. The results are given in the table below. Age Group Watch 11 p.m. News? 18 or less 19 to 35 36 to 54 55 or Older Total Yes 37 46 59 83 225 No 213 204 191 167 775 Total 250 250 250 250 1,000 (a) Let p1, p2, p3, and p4 be the proportions of all viewers in each age group who watch the station’s 11 p.m. news. If these proportions are equal, then whether a viewer watches the station’s 11 p.m. news is independent of the viewer’s age group. Therefore, we can test the null hypothesis H0 that p1, p2, p3, and p4 are equal by carrying out a chi-square test for independence. Perform this test by setting α = .05. (Round your answer to 3 decimal places.) χ2 = so H0: independence (b) Compute a 95 percent confidence interval for the difference between p1 and p4. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) 95% CI: [ , ]

Answer 1

Answer :

	18 or less	19 to 35	36 to 54	55 or older	Total
Yes	37	46	59	83	225
No	213	204	191	167	775
Total	250	250	250	250	1000

Minitab Steps

1. Click Stat → Tables → Cross Tabulation and Chi-Square.
2. A new window named “Cross Tabulation and Chi-Square” pops up.
3. Select “row variable” as “For rows.”
4. Select “column variable” as “For columns.”

• Click “OK” in the window named “Cross Tabulation and Chi-Square.”
• The Chi-square test results appear in the session window.

P-value:0.000 which is less than 0.04 so we Reject the H₀ hypothesis.

b) Difference between two proportions p1 Vs p4:

p1= 37/250= 0.148

p4= 83/250= 0.332

Critical z value = Z(0.05/2)= 1.96

-0.441,-0.25

Hope this will be helpful. Thanks and God Bless You :)