Question

The Speedy Oil Change Company advertises that the average mean time it takes to change a customer's oil is 10 minutes. After receiving complaints from dissatisfied customers, the management at Speedy Oil Change headquarters hired a researcher to investigate the complaints to determine if the oil change took significantly longer than 10- 8minutes. The researcher randomly investigates 20 oil changing jobs and computes thesample mean time to change a customer’s oil is 11.3 minutes with a sample standard deviation of 3.3 minutes. Based on this sample result, the researcher decides to conduct a hypothesis test to determine if Speed Oil Change Company’s claim is statistically too low atα = 5 %?

I. State the hypotheses (in words & symbols):
H0: ______________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________

Ha: ______________________________________________________________________________ ________________________________________________________________________________ _________________________________________________________________________________

II. Determine the model to test H0
a) Can you use a normal distribution for the Sampling Distribution model to perform this test? Please explain. If not, then what distribution could you use? __________________________________________________________________________________

_________________________________________________________________________________

b) Using the appropriate notation, state the MEAN & STD ERROR of the sampling distribution:

Mean: _______________________________________________________________________
STD Error: _______________________________________________________________________

III. Determine the Decision Rule:

State the decision rule: ____________________________________________________________ _________________________________________________________________________________

________________________________________________________________________________

___________________________________________________

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IV. Analyze the sample data:

Using the appropriate notation, state the sample result of the test, p-value and the test statistic.

sample result is: ____________________________________________________

p-value is: ______________________________________________________

test statistic is: _____________________________________________________

V. State the Conclusion: ___________________________________________________ _________________________________________________________________________________

Answer Question: Based on this sample result, can the researcher conclude that Speed Oil ChangeCompany’s claim is too low at α = 5 %? YOU MUST EXPLAIN YOUR ANSWER

_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

Answer 1

x̅ = 11.3, s = 3.3, n = 20

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In words:

H0: The population mean time it takes to change a customer's oil is 10 minutes

H0: The population mean time it takes to change a customer's oil is more than 10 minutes

In symbols:

Null and Alternative hypothesis:

Ho : µ = 10

H1 : µ > 10

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Yes, we can use a normal distribution for the Sampling Distribution model to perform this test as the sample is random and independent.

Mean =10

Standard error, se = s/√n = 3.3/√20 = 0.7379

df = n-1 = 19

Critical value :

Right tailed critical value, t-crit = ABS(T.INV(0.05, 19)) = 1.729

Reject Ho if t > 1.729

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Test statistic:

t = (x̅- µ)/(s/√n) = (11.3 - 10)/(3.3/√20) = 1.7618

p-value = T.DIST.RT(1.7618, 19) = 0.0471

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

There is enough evidence to conclude that the population mean time it takes to change a customer's oil is more than 10 minutes at 0.05 significance level.