Question

QUESTION 2 1)-2) Use the sample data below to test the hypotheses: HO: p1=p2=p3 H1: Not all population proportions are equal Response | 1 2 3 Total Yes 46 16 68 130 No 44 44 82 170 Total 90 60 150 300 At 2.5% level of significance, the conclusion is fail to reject HO No test No decision Reject HO LA

Answer 1

Solution Given Response 3 Total so 68 130 16 Yes 82 170 No 44 44 150 300 Total 90 60 Now to state the hull and alternative hypothesis Null hypothesis Ho: P = P2 = 1; Alternative hypothesis H, : Not all Population proportions are equal Here 1 2.5 loo L = 0.025 Now first to find the expected frequencies om each cell row total X column total Expected frequency Grand total

2 3 Total Response 130x90 130 X 60 130x150 300 Yes 130 3oo 3oo 39 26 = 65 No 170x90 1 ToX6o 170x150 300 300 300 170 34 - 85 Total 90 300 60 150 Now to find the x²-statistic We know that The formula of x ²statistic (o-E)? is given by E 2 (46-39² (16-26)? (68–65)? (44-51)? (44-34) 2 X + + t + 39 26 65 51 34 (82-85² + 85 2 q 2 2 34 85 65 51 49 85 х + + t 26 + + 39 100 t + t + 34 X12564 + 3.8462 + 0.1385+ 0.9608 + 2.9412+ 0.1059 x² = 9.249 X ² 49 51 39

x-statistic 9.249 Now to find the degrees of freedom degrees of freedom df = (2-1) (3-1) df = (1) (2) df = 2 2 X² Critical value =x & df -X 0.025, 2 7.378 Decision :- x ² statistic > x² Value critical 9.249 > 7.378 since x²-statistic is greater than x² critical value. So we reject the null significance, the conclusion is Reject to the "option-D" is is the correct answer hyethesis (h.) At 2.5%. level of Hence