91Ó°ÊÓ

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 $P_m≤P_w$

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.$\mathrm{Î\pm }=0.05$

ii. Conclusion: the null hypothesis must be rejected.

iii.$p-$value$>\mathrm{Î\pm }$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.