The National Center for Educational Statistics (NCES) reports that the average s

Question

The National Center for Educational Statistics (NCES) reports that the average score for 12 th graders who took the national reading test was 295 (on a scale of 1 to 500) ( source: nces.ed.gov). A random sample of 100 12 th graders in Blanchet County, Alabama, schools recently took the test. Students in the sample had an average score of 301. Given the following hypotheses, Ho: u = 295 (The mean score for the population of Blanchet 12 th graders is the same as the national average.) Ha : = 295 (The mean score for the population of Blanchet 12 th graders is not the same as the national average.)

a. Compute the p-value for the sample result in this two-tailed test. Assume the population standard deviation is 38 points.

b. Should you reject the null hypothesis at the 5% signicance level? Explain.

Explanation / Answer

(a)

Data:    

n = 100   

= 295   

s = 38   

x-bar = 301   

Hypotheses:   

Ho: = 295   

Ha: 295   

Decision Rule:   

= 0.05   

Lower Critical z- score = -1.959963985

Upper Critical z- score = 1.959963985

Reject Ho if |z| > 1.959963985

Test Statistic:   

SE = s/n = 38/100 = 3.8

z = (x-bar - )/SE = (301 - 295)/3.8 = 1.578947368

p- value = 0.11434813   

(b)

Decision (in terms of the hypotheses):

Since 1.578947368 < 1.959963985 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the mean is different from 295.

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