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Kay [80]
3 years ago
10

Suppose the national mean SAT score in mathematics was 510. In a random sample of 60 graduates from Stevens High, the mean SAT s

core 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?
Mathematics
1 answer:
zalisa [80]3 years ago
7 0

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, \bar{x} = 502

Sample size, n = 60

Sample standard deviation, s = 30

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

H_{0}: \mu = 510\\H_A: \mu \neq 510

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

Formula:

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

t_{stat} = \displaystyle\frac{502- 510}{\frac{30}{\sqrt{60}} } = -2.0655

Now,

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

Since,              

|t_{stat}| < |t_{critical}|

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.

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If the loan is paid off in the middle of the month, the interest due is reduced. Above, we have calculated interest based on a last payment made part way through the month. We rounded up, partly because of the ambiguity in the final payment.

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