Question

A trainer claims that a marathon runner's maximal volume oxygen uptake is greater than the average athlete. The average athlete has an average maximal volume uptake of 37.8 ml/kg. A random sample of 18 marathon runners has a mean of 41.2 and a standard deviation of 5.8 ml/kg. Test this claim at an alpha level of .05. What type of test are you going to perform and show all five steps of the hypothesis test including labeling the critical value and test value.

Answer 1

Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

We will use the t-test with 1 sample for this.

Step 1 :

Ho: Mu <= 37.8

Ha: Mu > 37.8

Step 2:

The t statistic will be used with alpha = .05

Step 3:

Null hypothesis is rejected if p-value is less than .05

Step 4:

Test statistic = (Xbar - Mu)/(Stdev/sqrt(n)) = (41.2-37.8)/(5.8/sqrt(18)) = 2.487

p-value at df = n-1 = 17 is .0118 i.e. less than .05

Step 5:

We reject Ho as p-value < .05, and conclude that average athlete has an average maximal volume uptake of more than 37.8 ml/kg.