Question

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1213 males​ surveyed, 179 responded that they had at least one tattoo. Of the 1031 females​ surveyed, 148 responded that they had at least one tattoo. Construct a 99​% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

Let p1 represent the proportion of males with tattoos and p2 represent the proportion of females with tattoos. Find the 99​% confidence interval for p1 - p2.

.

The lower bound is ?.

The upper bound is ?

​(Round to three decimal places as​ needed.)

Interpret the interval.

A. There is 99​% 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 males and females that have at least one tattoo.

B. There is a 99​% probability that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo.

C. There is a 99​% 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 males and females that have at least one tattoo.

D. There is 99​% confidence that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo.

Answer 1

solution:-

given that

males n1 = 1213 , x1 = 179

proportion p1 = x1/n1 = 179/1213 = 0.148

females n2 = 1031 , x2 = 148

proportion p2 = x2/n2 = 148/1031 = 0.144

the value of 99% confidence from z table is 2.576

confidence interval formula

=> (p1-p2) +/- z * sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2))

=> (0.148-0.144) +/- 2.576 * sqrt((0.148*(1-0.148)/1213) + (0.144*(1-0.144)/1031))

=> (-0.035 , 0.043)

the lower bound is -0.035

the upper bound is 0.043

Interpret the interval.

option: D. There is 99​% confidence that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo