Question

For the scenario below, identify the statistical test that can be used to solve the problem. Also, specify the appropriate hypotheses or formula and associated assumptions

30 female swimmers are to compete in a swim gala for two consecutive times. During the first gala, one of two types of swimming caps is to be used. During the second race, another type of swimming cap is to be used. The order in which a female swimmer wears a particular type of swimming cap is determined randomly. Our goal is to find out if the mean scores of swim times differs by swim caps used.  

Answer 1

Solution:-

We will conduct a matched-pairs t-test of the null hypothesis.

The appropriate hypotheses or formula are :-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_d = 0

Alternative hypothesis: u_d ≠ 0

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

DF = n - 1

Associated assumptions are :-

1) The sampling method for each sample is simple random sampling.

2) The test is conducted on paired data.

3) The sampling distribution is approximately normal.