1. Here are several situations in which there is an incorrect application of the ideas in statistical inference. Write a sentence or two in each case explaining what is wrong and why it is wrong.

(a) A significance test rejected the null hypothesis that the sample mean is equal to 500.

(b) A test preparation company wants to test that the average score of their students on the ACT is better than the national average score of 21.2. They state their null hypothesis as H₀: > 21.2.

(c) A study summary says that the results are statistically significant and the p-value = 0.98.

(d) The computed value for the test statistic is Z₀ = 0.018. Because this is less than 0.05, the null hypothesis is rejected.