Question

Shoes The AP Statistics class in Exercise 1 also asked an SRS of $20$boys at their school how many pairs of shoes they have. A $95\%$confidence interval for ${\mu }_G-{\mu }_B=$the true difference in the mean number of pairs of shoes for girls and

boys is $10.9to26.5$.

a. Interpret the confidence interval.

b. Does the confidence interval give convincing evidence of a difference in the true mean number of pairs of shoes for boys and girls at the school? Explain your answer.

Short answer

a. There is $95\%$confidence interval.

b. The confidence interval gives enough convincing evidence of a difference in the true mean number of pairs of shoes for boys and girls at the school.

Step-by-step solution

Given Information

It is given that for $95\%$confidence interval, true difference in mean number of shoes for boys and girls are$(10.9,26.5)$

a. Estimating Confidence Interval

From give data, there is $95\%$assurance that true mean number of pair of shoes of girls is greater than true mean number of pair of shoes for boys.

b. To Explain that the confidence interval gives convincing evidence for difference in the true mean number of pairs of shoes for boys and girls at the school

We can observe that confidence interval is containing zero. Hence, it is not likely that there is not any difference in mean number of pair of shoes for boys and girls. Hence, there is convincing evidence for difference in the true mean number of pairs of shoes for boys and girls at the school .