Question

1. Why do we need different formulas to calculate test statistics and obtain p-values? Select all that apply. V The choice of test statistic depends on whether data is randomly sampled or not; this determines the sampling distribution. The choice of test statistic is arbitrary, choose whichever seems easiest to use at the time. The choice of test statistic is up to the statistician. We can choose any of the given test statistics to test any of the hypotheses so far. ✓ The choice of test statistic depends on the hypotheses being tested, and each test statistic has its own sampling distribution. ✓ The choice of test statistic depends on the manner in which data was collected; the sampling distribution is correct only if conditions are met. 2. In this module, we have only presented t-test statistics. When could we use the standard normal distribution to find the p-values for the paired, 2-sample and pooled tests (assuming all conditions are met)? Select all that apply. U If the population standard deviations are known. U We could use the standard normal distribution (2) instead of the t any time. If the sample sizes are very large (100 or more). U We can use z if the samples are random, otherwise we must use t. U There are no conditions under which we could use a z two compare two population means.

Answer 1

1) We need different formulas to calculate test statistics and obtain p values because:

• the choice of the test statistic depends on the hypothesis being tested, and each test statistic has its own sampling distribution.
• the choice of the test statistic depends on the manner in which data was collected, the sampling distribution is correct only if conditions are met.

2) We could use the standard normal distribution to obtain the p value if :

• If the population standard deviations are known,
• If the sample sizes are very large