MATH 1342 Name ___________________________ Elementary Statistical Methods Lab Ch.10 – Inferential Statistics One Sample

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MATH 1342 Name ___________________________
Elementary Statistical Methods
Lab Ch.10 – Inferential Statistics One Sample
Critical Thinking; Communication Skills; Empirical/Quantitative
Skills
Suppose you are the manager of Speedy Oil Change which claims
that it will change the oil in
customers’ cars in less than 30 minutes on average. Further
suppose that several complaints have
been filed from customers stating that their oil change took
longer than 30 minutes. Upper-level
management at Speedy Oil Change headquarters has requested that
you investigate the complaints.
To begin your investigation, you randomly audit 36 oil changes
performed by Speedy Oil Change and
record the time each customer waited for the oil change. The
number of minutes to complete each of
the 36 oil changes is reported below.
42 29 19 11 10 27
41 27 22 26 28 32
17 15 25 35 32 22
13 31 17 30 33 25
18 24 28 21 40 19
34 30 14 23 22 10
In the questions below, you will test if the mean is
significantly less than 30 minutes at a significance
level of 0.01.
1. List the requirements that should be met for this hypothesis
test. Have the requirements been
met? Justify your answer.
2. Write the null and alternative hypothesis.
3. Calculate the test statistic and the P-value. Label each
accordingly.
4. Would you reject the null hypothesis? Justify your answer
using a complete sentence and proper
grammar.
5. Is the company fulfilling its promise to “change the oil in
customers’ cars in less than 30 minutes on
average?”
Lab Ch.9-10 continued
Unfortunately, Speedy Oil Change continues to get customer
complaints. As the manager, you feel
that perhaps more analysis is needed. You know that you are
likely to be asked “how much less than
30 minutes is our mean oil change?”
6. Construct a 98% confidence interval. Report this confidence
interval accurate to 1 decimal place.
7. State the point estimate and calculate the margin of
error.
8. Explain to your superiors how to interpret this interval.
9. Using the confidence interval you created, calculate the
range of values that answers the question
“how much less than 30 minutes is our mean oil change?”
10. In order to solve the customer complaints, should the
company be advertising the mean time to
completion or a guaranteed time to completion? If they should be
advertising a guaranteed time to
completion, what time might they advertise? Justify your
answers.