Question

SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 433 . Assume the population standard deviation is 115 .

(a) Construct a 99 % confidence interval for the mean mathematics SAT score for the entering freshman class. Round the answer to the nearest whole number.

Answer 1

The 99% confidence interval is
`403.33 <  \mu < 462.67`

Explanation:

From the question we are told that

The sample size is n = 100

The sample mean is
`\= x = 433`

The standard deviation is
`\sigma = 115`

From the question we are told the confidence level is 99% , hence the level of significance is

`\alpha = (100 - 99 ) \%`

=>
`\alpha = 0.01`

Generally from the normal distribution table the critical value of
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  2.58`

Generally the margin of error is mathematically represented as

`E = Z_{(\alpha )/(2) } *  (\sigma )/(√(n) )`

=>
`E = 2.58 *  (115 )/(√(100) )`

=>
`E = 29.67`

Generally 99% confidence interval is mathematically represented as

`\= x -E <  \mu <  \=x  +E`

=>
`433 -29.67 <  \mu < 433 + 29.67`

=>
`403.33 <  \mu < 462.67`