Question

A random sample of 400 men and 400 women was randomly selected and asked whether they planned to attend a concert in the next month. The results are listed below. Perform a homogeneity of proportions test to test the claim that the proportion of men who plan to attend a concert in the next month is the same as the proportion of women who plan to attend a concert in the next month. Use ? = 0.05.

	Men	Women
Plan to attend	230	255
Do not plan to attend	170	145

c) Find the sample test statistic.

d) Use either the P-value or Critical Value approach to conclude your test.

e) State your conclusion in the CONTEXT of the problem.

Answer 1

Ho : The proportions are same for both populations M : The proportions are not same for both populations Men W 230 Plan to attend Do not plan to attend Total omen Total 255 145 400 485 315 170 400 (Row Total) (Column Total) We calculate expected frequencies by: E- Grand Total Col-1 Col-2 485 400 800 315 400 800 485 400 800 315 400 Row-1 242.50 242.50 Row-2 157.50 800 157.50 To calculate chi-square test statistic we calculate this formula on each cell Observed Count Expected Count)2 Expected Count Observed Count Expected Count (0 E) 230 242.5 0.64433

255 170 145 242.5 157.5 157.5 0.64433 0.992063 0.992063 (O - E)2 3.272 787 Test statistic 3.273 Significance level 0.05 Degrees of freedom,df (r- 1) (c 1)- (2 1 (2-1) 1 Critical value 3.841 has area of 0.05 to its right. To find Xopen any Chi-square table, go across from 05 row df = v = 1 and down from column 0.05 and get 3.841 To get p-value, we can use excel function CHỈSQ. DIST. RT( 3.272787 , 1) 0.070 437 875 0.0704 Since test statistic is not greater than critical value we fail to reject ull hypothesis. At 5% level, there is NOT sufficient evidence that the proportions are different It is plausible that the proportion of men who plan to attend a concert in the next month is the same as the proportion of women who plan to attend a concert in the next month