Question

1. Independent simple random samples of 400 Hong Kong women and 380 Macao women were taken. Of Hong Kong women, 318 were found to be in the labor force; of the Macao women, 276 were found to be in the labor force. At the 5% significance level, do the data suggest that the labor-force participation rate of Hong Kong women is higher? Use the P-value approach to perform a hypothesis test.

Answer 1

i am denoting Hong Kong women group by 1 and Macao women group by 2.

given data and necessary calculations are:-

the pooled proportion be:-

hypothesis:-

[ claim ]

the test statistic be:-

the p value is :-

[ using standard normal table ]

decision:-

p value = 0.0122 < 0.05 (Alpha)

so, we reject the null hypothesis.

conclusion:-

there is sufficient evidence to claim that the labor-force participation rate of Hong Kong women is higher.

*** if you have any doubts about the problem please mention it in the comment box... if satisfied please LIKE.