Question

A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 259 students was x⎯⎯⎯ = 147 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 65 minutes in the population of all first-year students at this university. Use the survey result to give a 95% confidence interval for the mean study time of all first-year students. ___ to ___ ?

Can you also list step by step how to solve the problem on a calculator (TI-84 if possible)?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 147

Population standard deviation =    = 65

Sample size = n =259

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.05 = 1.96}

Margin of error = E = Z/2 * ( /n)

=1.96* (65 / 259 )

= 7.92

At 95% confidence interval estimate of the population mean is,

- E < < + E

147 - 7.92 < < 147 + 7.92

139.08 < < 154.92

(139.08 ,154.92)