Question

- Statistics -

In a cost-of-living study, weekly grocery expenses for families with one or two children were studied. A random sample of n=36 families was selected and the sample mean and standard deviation were found to be $204 and $18, respectively. Using a 5% level of significance, test that the average weekly grocery expenses for families with one or two children is more than $200, the average found from a previously conducted study. Make sure to include all of the steps of a hypothesis test.

Answer 1

Here we're testing the hypothesis:

For testing this hypothesis, we'll be using a one-sample t-test. The test statistic is given by:

Here the test statistic follows a t-distribution with n-1 = 35 degrees of freedom. Thus the p-value is P(T35>1.333)=0.0955.

The p-value here is less than 0.05, the level of significance. Thus we fail to reject the null hypothesis.

Hence we conclude that there is not enough evidence to support the claim that average weekly expenses are more than $200.