Question

Ten years ago, the average amount of time a family spent eating supper together was 27.8 minutes. A sociologist believes this average has decreased. She randomly selects a sample of 12 families and finds the sample average to be 24.307 minutes.

a) She also found sample standard deviation to be 8.27. Write null and alternative hypotheses to test her claim.

b) Which test should you run to test her claim? Conduct the test and report conclusion using a = 0.05. Show all steps of the tests, including formulas.

Answer 1

a)

H0: >= 27.8

Ha: < 27.8

b)

Since population standard is not known (that is sample standard deviation given) we use t test.

t = - / S / sqrt(n)

= 24.307 - 27.8 / 8.27 / sqrt(12)

= -1.463

This is test statistics value.

Critical value at 0.05 level for 11 df (df = n-1) is -1.796

Since test statistics > -1.796, we do not have sufficient evidence to reject H0.

We conclude at 0.05 level that we fail to support the claim that average has decreased.