Question

A new version of SAT is given to 1000 randomly selected high school seniors. Thesample mean test score is 1110, and the sample standard deviation is 123. Constructa 95% confidence interval for the population mean test score for high school seniors.

Answer 1

Answer: (1108.49 ; 1111.56)

Explanation:

confidence interval.

Sample mean (S) = 1110

Sample Size (N) = 1000

standard deviation (sd) = 123

confidence α= 1 - 0.95 = 0.05/2 = 0.025

Z distribution table

Zα= Z(0.025) = 0.4013

confidence interval

(S - Zα.×Sd/$\sqrt{N}$ ; S + Zα.×Sd/$\sqrt{N}$)

(1110 - 0.4013×(123/$\sqrt{1000}$) ; 1110 + 0.4013×(123/$\sqrt{1000}$)

(1108.491029 ; 1111.5608970091)

(1108.49 ; 1111.56)