Question

Dr. Chung, a renowned dietitian, has consistently proclaimed the benefits of a balanced breakfast. To substantiate his claim, he asks participants to go without breakfast for one week. The following week he asks the same participants to make sure they eat a complete breakfast. Following each week, Dr. Chung asks each participant to rate their productivity for that week Participant Performance with Breakfast Performance without Breakfast 5 What is the null hypothesis in the example above? What is the two-tailed research hypothesis in the example above? if Dr. Chung initially believed that productivity would improve after participants ate breakfast, how would he write the one-tailed null hypothesis? After following his sample for several weeks, Dr. Chung runs more statistics and determines a Cohen's d of 87 for athletes who ate breakfast. What does this statistic mean?

Answer 1

We have to test whether productivity depends on a balanced breakfast

Let $\mu1$ be the population mean productivity rating of people given a balanced breakfast

Let $\mu2$ be the population mean productivity rating of people without a balanced breakfast

The null hypothesis in the example is

Ho : μ1 = μ2

The two tailed research hypothesis for the above example is

Ha : μ1 ≠ μ2

Since Dr. Chung believed productivity would improve after a balanced breakfast $(\mu1)$

The null hypothesis is

Ho : μ1 ≥ μ2

Cohen's d is 0.87

Cohen's d determines the effect size indicating the standardized difference between two mans

Cohen suggested that d=0.2 be considered a 'small' effect size, 0.5 represents a 'medium' effect size and 0.8 a 'large' effect size. This means that if two groups' means don't differ by 0.2 standard deviations or more, the difference is trivial, even if it is statistically significant.   

In our example Cohen's d = 0.87

This is a large effect size indicating that the difference in the productivity mean ratings is large between the population which has had balanced breakfast and the one without breakfast.