Question

In order to estimate the average combined SAT score for students at a particular high school, a random sample of 100 students was selected and the sample mean was determined to be 870 with a sample standard deviation of 12 points.

a) Determine the error (for a 95% confidence interval) involved when trying to use the data from the sample to estimate the population.

b) Use the information in part A to help construct a 95% confidence interval estimate for the average combined SAT score for all students at the high school.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 870

Population standard deviation =    = 12

Sample size n =100

standard error=( /n) =(12 / 100) =1.2

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * (12 / 100)

= 2.3520
At 95% confidence interval estimate of the population mean
is,

- E < < + E

870 - 2.3520 <   < 870 + 2.3520

867.6480<   < 872.3520
(  867.6480, 872.3520)