A carpet company advertises that it will deliver your carpet within 15 days of p

Question

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The standard deviation of the population () is known to be 5.6 days.

a.         State the null and alternative hypotheses.

            b.   Using the critical value approach, test to determine if their advertisement is legitimate. Let = .05.

            c.   Using the p-value approach, test the hypotheses at the 5% level of significance.

Explanation / Answer

Given n=49, xbar=16.2, s=5.6

a. State the null and alternative hypotheses.

Ho: > =16.2
Ha:<16.2

b. Using the critical value approach, test to determine if their advertisement is legitimate. Let = .05.

The test statistic is

Z=(xbar-)/(s/n)

=(16.2-15)/(5.6/7)

=1.5

Given a=0.05, the critical value is |Z(0.05)|=1.645 (check standard normal table)

Since Z=1.5<1.645, we do not reject Ho.

c. Using the p-value approach, test the hypotheses at the 5% level of significance.

The p-value = P(Z<1.5) =0.9332 >0.05, we do not reject Ho.

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