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 ( σ) is known to be 5.6 days.

a. State the null and alternative hypotheses for a test to determine if their advertisement is legitimate.

b. Using the critical value approach, test the hypotheses. Let α = .05.

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

Answer 1

a.

Null Hypothesis H0: = 15

Altenative Hypothesis H0:   15

b.

Sample mean, = 16.2

Standard deviation σ = 5.6

Since we know the true population standard deviation we will conduct one sample z test.

Standard error of mean, SE = σ / = 5.6 / = 0.8

Test statistic, z = ( - ) / SE =  (16.2 - 15) / 0.8 = 1.5

Critical value of z at α = .05 is 1.96.

Since the test statistic is less than the critical value, we fail to reject null hypothesis H0 and conclude that there is no strong evidence to conclude that advertisement is not legitimate and average delivery time is not 15 days.

c.

For two-tail test, p-value = 2 * p(z > 1.5) =  0.1336

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence to conclude that advertisement is not legitimate and average delivery time is not 15 days.