Question

A district-wide test is used to measure math attitude in freshmen in high school students, with a mean of 78 and a standard deviation of 12. Thirty-six selected freshmen took the test and their mean score was 85. You are tasked to examine if these students are significantly different from the district test group

Answer 1

Explanation:

Given that

Population mean
`\mu=78`

std deviation
`\sigma =12` = 12

sample size n =36

Sample mean =
`\bar x = 85`

`H_0: \bar x = 85\\H_a: \bar x \\eq 85`

(Two tailed test)

Mean difference = 7

Std error =
`(\sigma)/(√(n) ) \\=(12)/(6) \\=2`

Since population std dev is known and n>30 we use Z test

Z statistic =
`(7)/(2) =3.5\\`

p value <0.001

Since p value is <0.01, at 1% significance level, we reject H0.

There is significant difference between sample mean and population mean.