Question

A college wants to know the lower limit of a two-sided 95% confidence interval for SAT scores on the Math section (range equals 200 to 800).

They sampled 400 students and found that the sample mean was 560 and the sample standard deviation was 35.

     Please show detail steps.

      Please type out response verses hand written.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 560

sample standard deviation = s = 35

sample size = n = 400

Degrees of freedom = df = n - 1 = 400 - 1 = 399

At 95% confidence level the t is,

= 1 - 0.95 = 0.05

/ 2 = 0.025

t _/2,df = t 0.025,399 = 1.966

Margin of error = E = t_/2,df * (s /n)

= 1.966 * ( 35 / 400 )

Margin of error = E = 3.44

The 95% lower limit confidence interval estimate of the population mean is,

- E

560 - 3.44 = 556.56

lower limit = 556.56