Average years f education are reported by social class based on data from the GSS 2018.

Mean Standard deviation N

Lower class 12.19 3.08 102

Working class 13.16 2.93 523

Middle class 14.60 2.88 498

Upper class 15.21 3.01 34

(a) Construct the 95% confidence interval for the mean number of years of education for lower and working class respondents.

(b) Construct the 99% confidence interval for the mean number of years of education for lower class and middle class respondents.

(c) As our confidence in the result increases, how does the size of the confidence interval change? Explain why this is so.