Question

A study of 50 people who were not on a diet showed that they consumed an average of 2200 calories in a day, with a standard deviation of 400 calories per day. For 40 people who were on a diet, they consumed an average of 2100 calories per day, with a standard deviation of 250 calories per day. Assume both populations are normally distributed. a) Test the claim that people on a diet consume fewer calories. b) Test the claim that people on a diet have a lower standard deviation in the number of calories they consume.

Answer 1

a) The standard error here is computed as:

Now as we are testing here whether people on a diet consume fewer calories, therefore the test statistic here is computed as:

For n₁ + n₂ - 2 = 88 degrees of freedom, the p-value here is obtained from the t distribution tables as:
p = P( t₈₈ > 1.45) = 0.0753

As the p-value here is 0.0753 > 0.05 which is considered the level of significance, therefore the test is not significant here at the 5% level of significance and we dont have sufficient evidence here that people on a diet consume fewer calories.

b) The test statistic here is computed as:

For n₁ - 1 = 49 and n₂ - 1 = 39 degrees of freedom, the p-value here is obtained from the F distribution tables as:

As the p-value here is 0.0015 < < 0.05, therefore the test is significant here and we have sufficient evidence here that people on a diet have a lower standard deviation in the number of calories they consume