Just Statistics ((Minitab)) Expert !!

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DSCI 346-01 F16: Chapter 9 On-Paper Assignments (20 points, each question = 10 pts.)

Begin each problem by re-writing the problem. Minitab is required; attach or include your output. Use Word; you may handwrite equations. You may want to refer to the Minitab handouts for Chapter 9 (on Canvas under Modules, Chapter 9 Handouts).

1. Recently, Pizza Parlor has begun receiving complaints from customers about the amount of

time they have to wait for their pizza deliveries. To address this issue, Pizza Parlor made some

operational changes and added more delivery people to its staff. The following data represent

a random sample of delivery times:

17 25 32 28 24 34 20 30 26 23 34 23

a. At the 0.05 level of significance, is there evidence that the mean delivery time is less than

30 minutes? Follow and show the 7 steps for hypothesis testing.

b. Determine the p-value and interpret its meaning.

c. What assumption must you make about the population distribution in order to conduct

the test in part a? Is the assumption valid? Use and include an appropriate graph from

Minitab. Write a couple of sentences supporting your answer.

d. Verify your results using Minitab.

2. The owner of a specialty coffee shop wants to study coffee purchasing habits of customers at

her shop. She randomly selects 60 customers during a certain week and finds that 32

customers say they “definitely will” recommend the specialty coffee shop to family and

friends.

a. At the 0.10 level of significance is there evidence that more than 50% of all customers say

they “definitely will” recommend the specialty coffee shop to family and friends? Follow

and show the 7 steps for hypothesis testing.

b. Determine the p-value and interpret its meaning.

c. What assumption must you make in order to conduct the test in part a? Demonstrate if

the assumption is met.

d. Verify your results for parts a and b using Minitab.

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Example Showing Form to Follow.

P-Value Approach – Results from Minitab 17

Restate Question or Problem

A bank brank has located in a commercial district of a city with the business objective of improving the process for servicing customer during the noon-to-1:00 P.M. lunch period. The waiting time (operationalized as the time the customer enters the line until he or she is reaches the teller window) of all customers during their hour is recorded over a period of a week. Data were collected from a random sample of 15 customers, and the results are organized as follows:

Waiting Time 4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20 4.50 6.10 0.38 5.12 6.46 6.19 3.79 (You do not have to rewrite the data). Questions: a. At the 5% level of significance, is there evidence that the population mean waiting time is less than 5

minutes? Follow and show the 7 steps. b. What assumption about the population distribution is needed in order to conduct the hypothesis

test? Is the assumption valid? Provide evidence to support your answer.

Part a: Showing the 7 Steps:

Step 1: State the research question or objective. At the 5% level of significance is there evidence that the

population mean waiting time is less than 5 minutes?

Step 2: Formulate the null and alternative hypotheses.

:Ho   ;

1 :H   

Step 3: Choose a significance level.

Significance level ( = 0.05.

Step 4: Determine the appropriate test statistic and its distribution. State the Decision Rule.

The test statistic is calc

X t

S

n

  , since population standard deviation, , is unknown.

Decision Rule (D.R.): Reject Ho if p-value < 0.05 () (using p-value approach)

Step 5: Calculate the test statistic and its p-value

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From Minitab: calc

X t

S

n

  = – 1.6867, p-value = 0.057

Step 6: Decision. Using the Decision Rule, compare p-value to and make a decision.

Fail to reject Ho since p-value of 0.057 is not less than of 0.05.

Step 7: Written Conclusion. Compare the decision to the hypotheses and write the conclusion.

Answer:

a) At the 5% level of significance there is insufficient evidence ( calc

t = – 1.6867, p-value = 0.057) that the

mean population waiting time is less than 5 minutes. Managerial implications: The business objective to improve waiting time indicates insufficient evidence that the waiting time has been significantly reduced. Thus, this process to improve waiting time did not meet the objective.

Minitab Results

One-Sample T: Waiting Time Test of mu = 5 vs < 5

95% Upper

Variable N Mean StDev SE Mean Bound T P

Waiting Time 15 4.287 1.638 0.423 5.032 -1.69 0.057

Answer b) From the histogram (or boxplot) of the sample data, it appears that the population may not be quite normally distributed. However, since the t-distribution is fairly robust with respect to the Normality Assumption, the results are deemed valid.

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1

0 X _

Ho

Waiting Time

F re

q u

e n

c y

Histogram of Waiting Time (with Ho and 95% t-confidence interval for the mean)