In: Statistics and Probability
A college admissions office takes a simple random sample of 120 entering freshmen and computes their mean SAT score to be 448. The population standard deviation is 116. Bsed on a 98%confidence interval mean, is it likely that the mean SAT score for entering freshmen is greater than 464? (first construct the 98% confidence interval)
Solution
Given that,
= 448
= 116
n = 120
At 98% confidence level the z is ,
= 1 - 98% = 1 - 0.98 = 0.02
/ 2 = 0.02 / 2 = 0.01
Z/2 = Z 0.01 = 2.326
Margin of error = E = Z/2* (/n)
= 2.326 * ( 116/ 120 )
= 24.63
At 98% confidence interval estimate of the population mean is,
- E < < + E
448 - 24.63< < 448 + 24.63
423.36 < < 472.63
(423.36, 472.63)