Hypothesis Testing

Week 5 Module Notes – Example 1 – Dependent Samples t-test.

Samples are dependent as two readings are taken for each subject.

Enter data into StatCrunch.

Click on Stat in the menubar, choose T Stats, then paired option. Select the variables for sample 1 and Sample 2.

We will subject our runners to a specific workout regimen we believe will make a statistically significant difference in their speed, thereby decreasing their 100-yard dash time.

Given the above expectation the speed will decrease, the difference between the two means (Time 1 – Time 2) will be greater than 0. Therefore µD > 0 option is selected. Now hit compute to get the output and p-value plot. Note in the module example calculations the difference (Time 2 – Time 1) is taken .

Paired T hypothesis test: μD = μ1 - μ2 : Mean of the difference between Time 1 and Time 2 H0 : μD = 0 HA : μD > 0

Since the p-value 0.0008 is less than the typical level of significance 0.05, there is evidence to reject the null hypothesis and favor the alternative which is μD > 0. We can conclude that the average speed has decreased after specific workout regimen.

Week 5 Module Notes – Example 2– Independent Samples t-test.

Samples are independent as there is no overlap between them.

Enter data into StatCrunch.

Click on Stat in the menubar, choose T Stats, then two sample and finally with data. Select the variables for sample 1 and Sample 2.

Our hypotheis will be that the runners in group A are faster than runners in group B.

Given the above expectation the speed will decrease, the difference between the two means (Time A – Time B) will be less than 0. Therefore μ1 - μ2 < 0 option is selected. Now hit compute to get the output and p-value plot.

Since the p-value 0.0547 is greater than the typical level of significance 0.05, there is no evidence to reject the null hypothesis. Therefore we can conclude there is no difference in the average run times between the two groups.