In: Statistics and Probability
In Example 23.3 Chapter 23 of the textbook, we tested whether the average fat lost from 1 year of dieting versus 1 year of exercise was equivalent. The study also measured lean body weight (muscle) lost or gained. The average for the 47 men who exercised was a gain of 0.1 kg, which can be thought of as a loss of –0.1 kg. The standard deviation was 2.2 kg. For the 42 men in the dieting group, there was an average loss of 1.3 kg, with a standard deviation of 2.6 kg. Considering a level of significance of 0.05 (5%), build a test of hypotheses to see whether the average lean body mass lost would be different between dieting and exercising for the population of men similar to the ones in this study.
a) Is this a one-sided or two-sided test?
b) Specify all four steps of your hypothesis test. Use the standard normal curve and Table 8.1 in Chapter 8 of the textbook to find an approximate p-value.