SOLUTION: Your company ships a lot of packages needing quick delivery and short notice. In the past, you have used Speedy Air Delivery Service, but you are beginning to receive complaints fr

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Question 588896: Your company ships a lot of packages needing quick delivery and short notice. In the past, you have used Speedy Air Delivery Service, but you are beginning to receive complaints from customers who say they are not receiving their packages on time. Speedy advertises that it delivers packages anywhere in the U.S. in an average of two days. To check Speedy�s claim, you select a random sample of 25 packages and find that the average delivery time for those 25 packages was 2.3 days.
1.Do you have sufficient evidence to accuse Speedy of false advertising? Explain why or why not. (For purposes of this discussion, we will assume that it is known that the standard deviation of package deliveries for Speedy is 0.5 days.)

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Hypothesis:
Ho: mu = 2
Ha: mu > 2

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Critical Z-value:
z = 1.64485
(use either a table or a calculator -- with significance level of alpha = 0.05, the default significance level)

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Test Statistic:

z = (xbar-mu)/(sigma/sqrt(n))

z = (2.3-2)/(0.5/sqrt(25))

z = (2.3-2)/(0.5/(5))

z = (2.3-2)/(0.1)

z = (0.3)/(0.1)

z = 3

The test statistic exceeds the critical value. So the test statistic lies in rejection region.

Conclusion: Reject Ho

So we can conclude that the mean delivery time is more than 2 days.

So you do have sufficient evidence to accuse Speedy of false advertising