Question

1. The Pew Research Center surveyed a sample of 41 students in 2000 and found the mean student loan amount for those college graduates was $26,682 with a sample standard deviation of $19,861. Construct the 95% t-confidence interval for the population mean student loan amount.

Answer 1

Solution:

Given:

Sample size = n = 41

Sample mean =

Sample Standard Deviation = s = 19,861

Confidence level = c = 95% = 0.95

We have to construct the 95% t-confidence interval for the population mean student loan amount.

Formula:

where

Find t_c value for c = 95% confidence level.

df = n - 1 = 41 - 1 = 40

Two tail area =1 - c = 1 - 0.95 = 0.05

t_c = 2.021

Thus

Thus

Thus a 95% t-confidence interval for the population mean student loan amount is between:

( $20,416.33 , $32,950.67 )