A college admissions office takes a simple random sample of 120 entering freshmen and computes their...

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)

Solutions

Expert Solution

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* ( $\sqrt$ /n)

= 2.326 * ( 116/ $\sqrt$ 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)

orchestra answered 1 year ago

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