Question

A manager of an e-commerce company would like to determine average delivery time of the products. A sample of 25 customers is taken. The average delivery time in the sample was four days. Suppose the delivery times are normally distributed with a standard deviation of 1.2 days.

a) Provide a 95 % confidence interval for the mean delivery time.

b) The manager claims that the average delivery time of their products does not exceed 3 days. Write the null and alternative hypothesis regarding to the claim of the manager.

c) Test the manager’s claim at 95 % confidence level.

d) Write the conclusion of your result

Answer 1

Answer:

Given that:

A manager of an e-commerce company would like to determine average delivery time of the products. A sample of 25 customers is taken. The average delivery time in the sample was four days.

sample size n = 25

sample mean = 4 days

population standard deviation = 1.2 days

a) Provide a 95 % confidence interval for the mean delivery time.

b) The manager claims that the average delivery time of their products does not exceed 3 days. Write the null and alternative hypothesis regarding to the claim of the manager.

The manager claims that the average delivery time of their products does not exceed 3 days. Write the null and alternative hypothesis regarding to the claim of the manager.

c) Test the manager’s claim at 95 % confidence level

test statistic

critical value =

since test statistic Z > -Z0.05 we fail to reject H0 and there is no significant evidence that mean delivery time is less than 3.

The 95% CI = (3.527 , 4.470) does not contain 3 and range does not contain values < 3, hence there is no significant evidence that mean delivery time is less than 3.

d) Write the conclusion of your result

There is no significant evidence that mean delivery time is less than 3.