Answer:
Correct option:
"All of the plausible values are positive, which is evidence that the proportion of men who play the lottery is greater than the proportion of women who play the lottery. "
Step-by-step explanation:
The hypothesis to test whether there is a significant difference between the proportion of men who played the lottery and the proportion of women who played the lottery can be defined as:
[tex]H_{o}:[/tex] There is no significant difference between the proportions, i.e.[tex]p_{M}-p_{W}=0[/tex]
[tex]H_{a}:[/tex] There is a significant difference between the proportions, i.e.
[tex]p_{M}-p_{W}\neq 0[/tex]
The 99% confidence interval to estimate the difference between the two proportion is,
[tex]CI_{p_{M}-p_{W}}=(0.0823, 0.1177)[/tex]
Decision Rule:
If the null hypothesis value is contained in the interval then the null hypothesis is accepted and if it is not contained in the interval the null hypothesis is rejected.
The 99% 99% confidence interval to estimate the difference between the two proportions consist of all positive values. The null hypothesis value, i.e. 0 is not in the interval.
Thus, the null hypothesis will be rejected.
Conclusion:
As all the values in the confidence interval is positive it implies that the proportion of men who played the lottery is more than the proportion of women who played the lottery.
The 1st option is correct.
