Question

The survey in the previous exercise also looked at possible differences in the proportions of white and Hispanic Internet users who used socialnetworking sites. They found that 870 of the 1331 white Internet users and 116 of the 147 Hispanics used social-networking sites. Do we have evidence at 1% level of a difference between the proportions of white and Hispanic Internet users who use social-networking sites? (Use pˆW?pˆHp^W?p^H for zz calculations.) pˆW(±0.0001)=p^W(±0.0001)= pˆH(±0.0001)=p^H(±0.0001)= z(±0.0001)=z(±0.0001)= PP-value (±±0.0001) = We don't have evidence that the proportions are different. We have evidence that the proportions are different.

Answer 1

Test for PuPh We want to test whether hypothesis: (Null Hypothesis) (Alternative Hypothesis, also called H1) This is two tailed test 870 P 1331 0.6536440.654 116 ph--~ 0.7891 16 0.789 147 Significance level, a 0.01 The test for difference in proportion is done by pooled sample proportion: Or (notations may differ) wnd i-1-j 870116 1331147 0.6671 18 q 0.332882 Pooled Standard Error: SE - nw nh

(0.667118) (0.332882) (0.667118) (0.332882) 0.040958 147 w - phu -h (0.653644) (0.789116 Test statistic, ZobservedSE 0.040958 nw nh -3.307598 -3.31 Test statistic =-3.31 Since this is upper tailed test, p-value-2 * P(Z < 1801-2 * P(Z <-3.31) 0.001 p-value 0.001 Note that exact p-value is: 0.0009409982 Decision : Since p-value < α, we reject the null hypothesis. Hence at 1% significance level, we have sufficient evidence to conclude that Pw is different than Ph We have evidence that the proportions are different