Suppose the national mean SAT score in mathematics was 510. In a random sample of 60 graduates from Stevens High, the mean SAT score in math was 502, with a standard deviation of 30. Test the claim that the mean SAT score for Stevens High graduates is the same as the national average. Test this claim at the 0.10 significance level.

(a) What type of test is this?

Question

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Answer :

ChiKesselman ChiKesselman · Answer 1 · 2025-04-06T04:47:18-04:00

Answer:

We accept the alternate hypothesis and conclude that mean SAT score for Stevens High graduates is not the same as the national average.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 510

Sample mean, [tex]\bar{x}[/tex] = 502

Sample size, n = 60

Sample standard deviation, s = 30

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 510\\H_A: \mu \neq 510[/tex]

We use Two-tailed t test to perform this hypothesis.

Formula:

[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n-1}} }[/tex] Putting all the values, we have

[tex]t_{stat} = \displaystyle\frac{502- 510}{\frac{30}{\sqrt{60}} } = -2.0655[/tex]

Now,

[tex]t_{critical} \text{ at 0.05 level of significance, 59 degree of freedom } = \pm 1.671[/tex]

Since,

[tex]|t_{stat}| < |t_{critical}|[/tex]

We reject the null hypothesis and fail to accept it.

We accept the alternate hypothesis and conclude that mean SAT score for Stevens High graduates is not the same as the national average.