Question

“Every user of statistics should understand the distinction between statistical significance and practical importance. A sufficiently large sample will declare very small effects statistically significant.”

In general, a population of elite female Canadian athletes were believed to be consuming an average 2403.7 kcal/day with population s.d. = sigma= 880 kcal/day. A nutritionist implemented a new diet among a sample of these athletes. Under the new diet, the sample of athletes had average daily intake of x-bar=2453.7 kcal/day. The standard deviation is assumed to remain the same with sigma x = 880 kcal/day.

Conduct a statistical test to test whether we have evidence that true average intake is larger than 2403.7 kcal/day for athletes on the new diet. Use these sample sizes:

1. n=100
2. n=500
3. n=1000

4. No alpha level was mentioned for the above problems, so we used the default level of alpha= 0.05. If the alpha level were given as 0.1 or 0.01, would statistical significance be impacted in questions a)-c)?

5. Why did we use a ‘one-sided’ test for this problem?

Answer 1