Question

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?

a) Yes, the proportion of males has reached the proportion of females.

b) No, the proportion of males has not reached the proportion of females.

c) Both a,b,and c

d) None of the above

Answer 1

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. I believe that the proportion of males has not reached the proportion of females. Thus the correct option is (b).

Step-by-step explanation:

Joan Nguyen's claim is based on the comparison of proportions of college-age males and females with at least one pierced ear. To evaluate this, we can calculate the proportions for both groups:

For males:

`\[ \text{Proportion of males with pierced ear} = \frac{\text{Number of males with pierced ear}}{\text{Total number of males}} \]`

`\[ \text{Proportion of males with pierced ear} = (20)/(107) \]`

For females:

`\[ \text{Proportion of females with pierced ear} = \frac{\text{Number of females with pierced ear}}{\text{Total number of females}} \]`

`\[ \text{Proportion of females with pierced ear} = (47)/(92) \]`

Comparing the two proportions:

`\[ (20)/(107) \\eq (47)/(92) \]`

The proportions are not equal, indicating that the claim is not supported by the survey data. Therefore, the correct answer is b) No, the proportion of males has not reached the proportion of females.

It's essential to consider the actual percentages to understand the disparity. The proportion of males with pierced ears (18.69%) is significantly lower than the proportion of females with pierced ears (51.09%). This substantial difference rejects Joan Nguyen's assertion that the proportions are equal. The survey data suggests a notable gender difference in the prevalence of pierced ears among college students.