Question

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. The 95% confidence interval for the population mean SAT score is:__________

Answer 1

Answer:

1341.2<x<1458.8

Step-by-step explanation:

Given

sample size n = 64

standard deviation = 240

average mean = 1400

z score at 95% CI = 1.96

Required

confidence interval

Confidence interval = xbar ± (z*s/√n)

CI = 1400 ± (1.96*240/√64)

CI = 1400 ± (1.96*240/8)

CI = 1400 ± (1.96*30)

CI = 1400 ± 58.8

CI = (1400-58.8, 1400+58.8)

CI = (1341.2, 1458.8)

Hence the confidence interval for the population is 1341.2<x<1458.8