Question

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1209 males​ surveyed, 183 responded that they had at least one tattoo. Of the 1089 females​ surveyed, 133 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 p 1 represent the proportion of males with tattoos and p 2 represent the proportion of females with tattoos. Find the 99​% confidence interval for p 1 minus p 2. The lower bound is nothing. The upper bound is nothing. ​(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

i am denoting males by group 1 and females by group 2.

given data and necessary calculations are :-

z critical value for 99% confidence level, both tailed test be:-

the 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 is:-

interpretation:-

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. (C)

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