A marketing consulting company has historically averaged 46 days on receiving payment from their clients. To improve cash flow, the manager was presented with an incentive bonus if she could reduce the average time it takes to receive payment. A random sample of 16 projects showed the mean time to receive payment is 38 days with a standard deviation of 10 days. Assume these times are approximately normally distributed. Is there enough evidence to conclude that the average time to receive payment has been reduced? Test the hypothesis at the 5% level of significance.

Test the hypothesis at the5% level of significance.

Question 1: Define the status quo used for the hypotheses.

(a) Which of the following are you examining? (Mean or Proportion)

(b) What is the "status quo" used in the null hypothesis?

Question 2: Which of the following is thenull hypothesis?

H₀:Mean/Proportion < Status quo

H₀:Mean/Proportion > Status quo

H₀:Mean/Proportion Status quo

H₀:Mean/Proportion = Status quo

Question 3: Which of the following is thealternate hypothesis?

H_A:Mean/Proportion = Status quo

H_A:Mean/Proportion > Status quo

H_A:Mean/Proportion < Status quo

H_A:Mean/Proportion Status quo

Question 4: To test the hypotheses, which distribution should you use?

(Normal) z-distribution

t-distribution

None of the above can be used

Question 5: What is the critical value for this hypothesis test (i.e. the z-score or t-score that defines the rejection zone)?

(Iftwo-tailed test, just write value of critical value, ignoring sign. Ifone-tailed test, include the sign)

Question 6: Which of the following most accurately states the rejection criterion?

a) Reject the null hypothesis, H₀, if thetest score < (negative) critical valueortest score > (positive) critical value

b) Reject the null hypothesis, H₀, if thetest score < critical value

c) Reject the null hypothesis, H₀, if thetest score > critical value

d) Reject the null hypothesis, H₀, if thetest score is between the critical values(between thenegative critical value and the positive critical value)

Question 7: What is the test statistic? (i.e. z-score or t-score from test results)

Question 8: Which of the following apply? (Select ALL that apply)

REJECT H₀

Do NOT reject H₀

test statistic critical value

test statistic < critical value

test statistic > critical value

test statistic is between the critical values

Question 9: Which of the following would be a good concluding statement for this hypothesis test?

a) No, there is NOT enough evidence to conclude that the average time to receive payment has been reduced.

b) No, the new sample results and the previous results are NOT different.

c) Yes, the new sample results and the previous results are different.

d) Yes, there is enough evidence to conclude that the average time to receive payment has been reduced.

Question 10: Which of the following statements is MOST accurate?

a) There is LESS than 5% likelihood that the decrease in time to receive payments was due to random fluctuations.

b) There is MORE than 5% likelihood that the decrease in time to receive payments was due to random fluctuations.

c) There is LESS than 0.5% likelihood that the decrease in time to receive payments was due to random fluctuations.

d) There is MORE than 10% likelihood that the decrease in time to receive payments was due to random fluctuations.

e) There is LESS than 1% likelihood that the decrease in time to receive payments was due to random fluctuations.

f) There is LESS than 2.5% likelihood that the decrease in time to receive payments was due to random fluctuations.