Question

2. Use the GSS 2014 data on education from Chapter 5 ("The Normal Distribution"), Exercise 5. 12.11 Mean Standard Deviation Lower class 2.83 122 Working class 13.01 2.91 541 Middle class 14.99 2.93 475 Upper class 15.44 2.83 a. Construct the 95% confidence interval for the mean number of years of education for lower-class 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. 34

Answer 1

Write the formula to construct the 95% confidence interval for the mean number of years as follows:

           

Here,

M is the sample mean

Z is the Z statistic determined by confidence level

$B3wBXlRNR8t+Dg0AAAAASUVORK5CYII=$ is the standard error

a)

Construct the 95% confidence interval for the mean number of years of education for lower class as follows:

            $0f8lR5tGPQvV0AAAAASUVORK5CYII=$

Thus, the mean number of years of education for lower class is.

Construct the 95% confidence interval for the mean number of years of education for working class as follows:

           

Thus, the mean number of years of education for working class is.

b)

Construct the 99% confidence interval for the mean number of years of education for lower class as follows:

           

Thus, the mean number of years of education for lower class is.

Construct the 99% confidence interval for the mean number of years of education for working class as follows:

           

Thus, the mean number of years of education for working class is.

c)

It can be seen from the above calculations that, as the confidence in the results increases, the size of the confidence interval increases as we