Question

Item Bazaar is an internet-based business and advertises that it fulfills customers’ orders in less than 3 business days. Periodically, the operations manager selects a random sample of customer orders and determines the number of business days required to fill the orders. On one occasion when a sample of 44 orders was selected, the average number of business days was 2.80. Based on extensive data from similar companies, the population standard deviation is known to be equal to 0.75 days. Using ? = .03, does it appear that the standard of filling customers’ orders in less than three business days is being met? Do a complete and appropriate hypothesis test.

Step 1 (Hypotheses)

H₀:  (Click to select)?px-barns??  (Click to select)=??>?<  

H_A:  (Click to select)?x-bar?p?sn  (Click to select)=??>?<  

Step 2 (Decision rule)

Using only the appropriate statistical table in your textbook, the critical value for rejecting H₀ is (Click to select)+-± . (report your answer to 2 decimal places, using conventional rounding rules)

Step 3 (Test statistic)

Using the sample data, the calculated value of the test statistic is (Click to select)+-± . (report your answer to 2 decimal places, using conventional rounding rules)

Step 4 (Evaluate the null hypothesis)

Should the null hypothesis be rejected?  (Click to select)yesno

Step 5 (Practical conclusion)

Should Item Bazaar conclude that the standard of filling customers’ orders in less than three calendar days is being met? (Click to select)yesno

Using only the appropriate statistical table in your textbook, what is the p-value of this hypothesis test?  

Answer:  (Report your answer to 4 decimal places, using conventional rounding rules)

Answer 1

Step-1:

Let be the population mean days to fulfill customer's order. We want to test:

Step-2:

Decision Rule: As the test is left tailed test and population standard deviation is known, our test-statistic would be a Z-statistic, so, we will reject at level of significance if

Step-3:

The observed value of test statistic

Step-4:

As - 1.769 > -1.88, we fail to reject null hypothesis at 3% level of significance. Answer - NO

Step-5:

Thus, we conclude that there is no compelling evidence for the company to establish that they fulfill customer's order in less than 3 days. . Answer - NO

p-value = P(Z < -1.769) = 0.0385