Question

The National Center for Educational Statistics (NCES) reports that the average score for 12th 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 12th graders in Blanchet County, Alabama, schools recently took the test. Students in the sample had an average score of 301. Given the following hypotheses, H0: ? ? 295 (The mean score for the population of Blanchet 12th graders is the same as the national average.) Ha: ? ? 295 (The mean score for the population of Blanchet 12th 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% significance level? Explain.

Answer 1

$H_{0}:\mu = 295$

$H_{a}:\mu \neq 295$

a) The test statistic is

$z = \frac{\bar x - \mu}{\sigma/\sqrt n}$

  $= \frac{301 - 295}{38/\sqrt {100}}$

  

P-value = 2 * P(Z > 1.58)

= 2 * (1 - P(Z < 1.58))

= 2 * (1 - 0.9429)

= 0.1142

b) Since the P-value is greater than the significance level (0.1142 > 0.05), so we should not reject the null hypothesis.