Question

When checking if weight loss is greater than 10 lbs per week for a particular population of weight between 130 and 140 lbs- a random sample shows weight loss of 12, 15, 19, 2, 8, 14 and 9 lbs.

If using the t-test to test if the average weight loss is greater than 10 lbs at 5% significance level, what is the p-value? You should use a one-sided test.

Answer 1

As we are testing here whether the weight loss is more than 10 lbs in the week, therefore this is a one tailed positive tailed t test. First we compute the sample mean and standard deviation for the given data using the following table:

The sample mean here is first computed as: (Second column sum )

Now using this the sample standard deviation is computed as: ( last column )

Therefore now the test statistic is computed as:

Now as this is a one tailed test, for n-1 = 6 degrees of freedom, the p-value here is computed as:

p = P( t₆ > 0.6152 ) = 0.2805

As the p-value here is 0.2805 > 0.05 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the weight loss is more than 10 lbs mean per week.