Question

a survey asked, how many tattoos do you currently have on your body? of the 1212 men surveyed, 179 responded that they had at least one tattoo. of the 1068 women surveyed, 143 responded that they had at least one tattoo. construct a 90% confidence interval to judge whether the proportion of men that have at least one tattoo differs significantly from the proportion of women that have at least one tattoo. interpret the interval. let ( p_1 ) represent the proportion of men with tattoos and ( p_2 ) represent the proportion of women with tattoos. find the 90% confidence interval for ( p_1 - p_2 ). the lower bound is -0.011. the upper bound is 0.039. (round to three decimal places as needed.) interpret the interval. choose the correct answer. a. there is 90% confidence that the difference of the proportions is in the interval. conclude that there is insufficient evidence of a significant difference in the proportion of men and women that have at least one tattoo. b. there is 90% confidence that the difference of the proportions is in the interval. conclude that there is a significant difference in the proportion of men and women that have at least one tattoo. c. there is a 90% probability that the difference of the proportions is in the interval. conclude that there is a significant difference in the proportion of men and women that have at least one tattoo. d. there is a 90% probability that the difference of the proportions is in the interval. conclude that there is insufficient evidence of a significant difference in the proportion of men and women that have at least one tattoo.

Explanation:

A confidence interval gives a range of values within which the true difference in proportions is likely to lie. A 90% confidence interval means that if we were to repeat the sampling process many times, 90% of the intervals constructed would contain the true difference. If the interval contains 0, it suggests there may not be a significant difference. Here, the interval for \(p_1 - p_2\) is \((- 0.011,0.039)\), which includes 0.

Answer:

A. There is 90% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of men and women that have at least one tattoo.