Question

#3 In 1990 and 2004, NAEP tested the 17-year-olds on the mathematics as well reading. The average score went up from 305 to 307. you may assume the NAEP took simple random samples of size 1,000 in each of the two years; the SD for the 1990 data was 34, and the SD for the 2004 data was 27. Can the difference between the 305 and 307 be explained as a chance variation

Answer 1

The standard error is first computed here as:

Now the test statistic here is computed as:

Now as this is a two tailed test for n₁ + n₂ - 2 = 1998 degrees of freedom, we get the p-value here as:

p = 2P(t₁₉₉₈ > 1.4567) = 2*0.0727 = 0.1454

As the p-value here is large, this difference here could be by chance as the test is not significant here.

Therefore there is no evidence here to support the claim that the difference is significant. It could have been by chance.