Final answer:
The Wilcoxon signed-rank test can be approximated by a z-test when the number of non-zero differences is at least 20 (option c), and in hypothesis testing, if the p-value is greater than alpha, the correct decision is to not reject the null hypothesis.
Step-by-step explanation:
The Wilcoxon signed-rank test for one sample can be approximated by a z-test when the number of non-zero differences, represented as 'n', is sufficiently large. While there is no definitive rule for when the approximation becomes acceptable, it is commonly recommended that for the approximation to be valid, 'n' should be at least 20. This is because as 'n' increases, the distribution of the Wilcoxon signed-ranks becomes more symmetrical and more similar to the normal distribution, which is a requirement for the z-test to be an appropriate approximation.
In making decisions about hypothesis testing, we look at the significance level, often denoted as alpha (α), and compare it to the p-value. If the p-value is less than or equal to α, we reject the null hypothesis. Conversely, if the p-value is greater than α, we do not reject the null hypothesis.