Question

US average math SAT scores follow a normal distribution with a mean of 505 and a standard deviation of 112. A sample of 64 entering Univ. of TN students revealed an average score of 477. Test the claim that the scores of UT students are less than the US average at the 0.05 level of significance.

Answer 1

The claim that the scores of UT students are less than the US average is wrong

Explanation:

Given : Sample size = 64

Standard deviation = 112

Mean = 505

Average score = 477

To Find : Test the claim that the scores of UT students are less than the US average at the 0.05 level of significance.

Solution:

Sample size = 64

n > 30

So we will use z test

`H_0:\mu \geq 477\\H_a:\mu < 477`

Formula :
`z=(x-\mu)/((\sigma)/(√(n)))`

`z=(505-477)/((112)/(√(64)))`

`z=2`

Refer the z table for p value

p value = 0.9772

α=0.05

p value > α

So, we accept the null hypothesis

Hence The claim that the scores of UT students are less than the US average is wrong