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Sav [38]
3 years ago
8

US average math SAT scores follow a normal distribution with a mean of 505 and a standard deviation of 112. A sample of 64 enter

ing 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.
Mathematics
1 answer:
Hitman42 [59]3 years ago
3 0

Answer:

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

Step-by-step 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=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}

z=\frac{505-477}{\frac{112}{\sqrt{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

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