Question

A restaurant claims the customers receive their food in less than 16 minutes. A random sample of 39 customers finds a mean wait time for food to be 15.8 minutes with a standard deviation of 4.9 minutes. At α = 0.04, what type of test is this and can you support the organizations’ claim using the test statistic?

Claim is the alternative, reject the null so support the claim as test statistic (-0.25) is in the rejection region defined by the critical value (-2.05)

Claim is the null, fail to reject the null so support the claim as test statistic (-0.25) is not in the rejection region defined by the critical value (-1.75)

Claim is the null, reject the null so cannot support the claim as test statistic (-0.25) is in the rejection region defined by the critical value (-2.05)

Claim is the alternative, fail to reject the null so cannot support the claim as test statistic (-0.25) is not in the rejection region defined by the critical value (-1.75)

Answer 1

Hypotheses are:

Since population standard deviation is unknown and hypothesis test population mean so t test should be used. Here sample size is large so we can assume that sampling distribution of sample mean is normal.

Here we have following information:

So test statitics will be

Here test is left tailed and degree of freedom of the test is df=n-1=39-1=38.

So for a = 0.04, critical value of the test is -1.799.

Rejection region: if test statistics value is less than -1.799 we reject the null hypothesis.

Since test statistics does not lie in critical region so we fail to reject the null hypothesis.

Correct option:

Claim is the alternative, fail to reject the null so cannot support the claim as test statistic (-0.25) is not in the rejection region defined by the critical value (-1.75)