Question

If a school district takes a random sample of 78 Math SAT scores and finds that the average is 461, and knowing that the population standard deviation of Math SAT scores is intended to be 100. Find a 99% confidence interval for the mean math SAT score for this district.

≤μ≤

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 461

Population standard deviation =    = 100
Sample size = n =78

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

= 2.576* ( 100/ 78)

= 29.17

At 99% confidence interval is,

- E < < + E

461-29.17 < < 461+29.17

431.83≤μ≤ 490.17