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

Answer:

Step-by-step explanation:

Given that

Population mean $\mu=78$

std deviation $\sigma =12$  = 12

sample size n =36

Sample mean = $\bar x = 85$

$H_0: \bar x = 85\\H_a: \bar x \neq 85$

(Two tailed test)

Mean difference = 7

Std error =$\frac{\sigma}{\sqrt{n} } \\=\frac{12}{6} \\=2$

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

Z statistic = $\frac{7}{2} =3.5$

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.