Joan Nguyen recently claimed that the proportion of college-age males with at least one pierced ear is as high as the proportion of college-age females. She conducted a survey in her classes. Out of $107$males, $20$had at least one pierced ear. Out of $92$females, $47$had at least one pierced ear. Do you believe that the proportion of males has reached the proportion of females?

Given in the question that, Joan Nguyen recently claimed that the proportion of college-age males with at least one pierced ear is as high as the proportion of college-age females. She conducted a survey in her classes. Out of$107$males, $20$had at least one pierced ear. Out of $92$females, $47$ had at least one pierced ear. We need to check that whether the proportion of males has reached the proportion of females.

a. The null hypothesis is defined as $P_m\le P_w$

a. The null hypothesis is defined as $P_m>P_w$represents an alternative hypothesis. .

c. The difference in the proportions of women and men who have at least one pierced ear is a random variable.

d. Normal distribution.

e. Fill in all requirements using Minitab's two sample t test option.

The result will be

Test results statistics $-5.04$

f. The output has a $p$-value of $1.00$.

g.The graph of the p value is unnecessary because the value is $1.00$.

i.$\alpha =0.05$

ii. Conclusion: the null hypothesis must be rejected.

iii.$p-$value$>\alpha$is the reason for the decision.

iv. Conclusion: There is enough information to establish that the proportions of males and females with at least one pierced ear differ at the $5\%$level of significance.