Question

Question 1

You are the manager of a fast-food restaurant operating in a city. It is known that the fast-food delivery time in the city is normally distributed with a mean not exceeding 8 minutes and a standard deviation of 1.5 minutes. You select a random sample of 30 deliveries from your restaurant. The sample mean delivery time is 8.6 minutes, and you wonder if the mean has increased over 8 minutes.

a. What are the hypotheses that the manager would use to conduct a hypothesis test to see if the population mean length of delivery time is greater than 8 minutes?

H0:

H1:

b. Determine the appropriate test statistic and state the appropriate test used and reason. Keep at least 2 decimal places. Show work. A loss of marks will result for not showing work even if your answer is correct.

Appropriate test used and reason:

Test Statistic

c. Find the critical value(s) of the test statistic at the 0.01 level of significance. Keep at least 2 decimal places. Show work. A loss of marks will result for not showing work even if your answer is correct.

Critical Value(s)

d. Is there evidence that the population mean amount is greater than 8 minutes (use α = 0.01)? Explain by providing your decision with reasons.

e. Compute the p-value and interpret its meaning. Keep at least 4 decimal places. Show work. A loss of marks will result for not showing work even if your answer is correct.

p-Value

f. Suppose the population mean is 8 minutes and the population standard deviation is 1.5 minutes.

Based on a random sample of 30 deliveries, there is a 6% chance that the mean delivery time

is above …

minutes

Show work. A loss of marks will result for not showing work even if your answer is correct.

Answer 1

Given
X bar	8.6
μ0	8
σ	1.5
n	30

Z test why because population standard deviation is known

a) Hypothesis :		α=	0.01
Ho:	μ1​ = μ0
Ha:	μ1​ > μ0
c) Z Critical Value :
Zc	2.326347874	NORM.S.INV(1-α)	RIGHT
Zs	>=	Zc	RIGHT	To reject
b) Test :
Z	2.19089023	(X bar-μ )/(σ/SQRT(n))
e) P value :
P value	0.014229868	1-NORM.S.DIST(z,true)	RIGHT
d) Decision :
P value	>	α	Do not reject

Conclusion:

There is not enough evidence to claim that the population mean amount is greater than 8 minutes

f)

Given, μ = 8 and σ = 1.5

P = μ + Zc*σ

α = 0.06

Zc = 1.55 (Use Z table)

P = 8+/-1.55*1.5

P94 = 10.325

P6 = 5.675

Mean delivery time is above 5.675 and below 10.325