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You have the NAEP quantitative scores for an SRS of 800 young men. You plan to test hypotheses about the population mean score, Ho: u=280 and Ha: u < 280 at the 1% level of significance. The population standard deviation is known to be = 50
The z statistic is z= x - 280/(50/sqrt800)

A. What is the rule for rejecting Ho in terms of z?

B. What is the rule for rejecting Ho restated in terms of the sample mean?

C. You want to know whether this test will usually reject Ho when the true population mean is 275, 5 points lower than the null hypothesis claims. Answer this question by calculating the power when u=275.


TS Contributor
A. What does z have to be in order to reject Ho at a 1% level of significance? Or, 99% confidence?

B. What value of x does the answer in A. lead you to? Solve for x after plugging z into your equation:

z= x - 280/(50/sqrt800)

C. Here you need to figure out what percentage of the normal curve will fall into the rejection region if the mean is 275.

Hint: From the original question, the rejection region is the area outside of the 99% confidence interval for u=280. By shifting the mean to 275 (and therefore, shifting the whole curve or distribution by -5), a lot more of the curve will fall into the rejection region - figure out exactly how much, and you have your answer.
Here's what I came up with.

A. z must be < or = to 2.326

B. x>or = to 280+2.326(50/sqrt800)= x<or=to 284.11

C. 275-280/(50/sqrt800)= -2.82 .0024 so .9976 (yes it will usually reject Ho).

I don't know if this is correct but thanks for the help it is much appreciated.
Last edited:


TS Contributor
Sorry - made a mistake here:

A. Looks OK

B. x must be <= 275.89

C. You need to draw two curves here:

-one with a mean of 280, std dev of 50, and shade the rejection region for 99% confidence

-then draw another one with mean 275 and std dev 50 --> what percentage of this curve falls in the rejection region of the first curve? - that's the answer.


TS Contributor
Since the null hypothesis is u=280, and the alternative hypothesis is u is less than 280, we need evidence that shows that u is "low enough" or less than 280 by a large enough amount.

Ho: u=280 and Ha: u < 280