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Lesson 13 Essay
Pengjun Zhou (PEN2159797)
GBS221 14812 Summer 1 2017
Submission 1
9/23/2017 6:00:58 PM
Score 26/30
Due Date 09/16/2017
Submitted 9/23/2017 6:00:58 PM
Status Graded 9/24/2017 9:03:52 AM
Total Score 26/30
Question 1
Using the New Call Center Data
(https://qmem.riosalado.edu/myrepository_res/gbs/gbs221/Lesson13_NewCallCenterData.xlsx), provide a
summary report for the vice president including the following information in an essay with a minimum of 500
words:
Using the two-sample hypothesis test comparing old call time to new call time at a .05 level of
significance, discuss the hypothesis test assumptions and tests used. Provide the test statistic and pvalue in your response. Evaluate the results of the hypothesis test with the scenario. Provide
recommendations for the vice president.
Using new call time and coded quality, develop a prediction equation for new call time. Evaluate the
model and discuss the coefficient of determination, significance, and use the prediction equation to
predict a call time if there is a defect.
Evaluate whether the new call time meets customer specification. As stated in a previous lesson,
customers indicated they did not want a call time longer than 7.5 minutes. Assume a standard deviation
of 2 min is acceptable. Is the call center now meeting the customer specifications? If not where is the
specification not being met? Explain your answers.
Response to Question 1
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For solving two-sample hypothesis test, we use z-test. We have two assumptions listed based on this
case, the null hypothesis is the sample average of old call and new call are same; the alternative
hypothesis is the sample average of old call and new call are not same. Then we start our calculations.
We need the sample mean first, do we use the sum of old calls/the sample size of old calls which
equals 11.066. Same calculation function for the new call, we get 8.853 for the mean of new calls. The
sample variance is calculated through the calculator which is 11.384 for old calls and 7.28 for new calls.
Now we assume old calls as x and new calls as y. The formula of defining test statistic is t=(meanxmeany) / [s*sqrt(1/nx+1/ny)], where s=sqrt[ (nx*s^2x +ny*s^2y)/(nx+ny-2) ], which is
[(150*11.384+150*7.28)/(15+150-2)=sqrt9.39=3.06. After that we can input all the data to the formula.
We have (11.066-8.853)/[3.06*sqrt(1/150+1/150)], 6.269 is the final answer for the test statistic. Now
the critical value at 0.05 level of significant is 2.262. Since 6.269>2.262, we accept the alternative
hypothesis that the sample average of old call and the new call are not same. As per the test, verify for
the improvement in the new call on the basis of average test and recommend to the vice president.
“A correlation coefficient indicated both the strength and direction of the linear relationship between an
independent and dependent variable” (Donnelly, 2015). We can perform a hypothesis test to determine
if the population correlation coefficient is significantly different from zero based on the sample
correlation coefficient. We use the regression equation to fit a prediction equation for new call data with
code quality. The formula for the regression equation is Y=a+bz, where z is the coded quality which
value is 0 or 1. “The regression equation provides a point estimate for a dependent variable, given the
value of an independent variable” (Donnelly, 2015). Based on the data we have, the sum of z*y is
142.8, the sum of z is 16, the sum of z^2 is 16. By inputting the data above within the formula b=(n *
sum of z*y – sum of y*sum of z)/n* sum of z^2 – mean of z^2 = (150*142.8-1328*16)/[150*16(0.106)^2]=0.0716; a=sum of y/n – b*(sum of z / n)= 1328/150-0.0716*(16/50)=8.8454. So the
prediction equation for new call is Y=8.8454+0.0716*1=8.917.
To test the customer satisfaction, when the average call duration is 7.5 min with a standard deviation of
2 min is acceptable, we apple z test for customer satisfaction on the basis of sample mean Y=8.853.
We assume the null hypothesis is uy=7.5, the alternative hypothesis is uy not equal to 7.5. The formula
of calculating the z test is (meany – uy)/s*sqrt(ny). By inputting the data, we get 8.27 as the result. With
the 0.05 level if significance, the critical p value is 1.96. Since Zobserved is greater than Ztabulated, we
accept the alternative hypothesis that the sample average of old call is not same. For the
recommendation, it is important to verify the improvement in the new call on the basis of average test.
Reference:
Donnelly, R. A. (2015). Business statistics (2nd ed.). Upper Saddle River, NJ: Pearson.
Words: 528 Characters: 2657
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SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.009179
R Square
0.00
Adjusted R
-0.00667
Square
Standard Error 2.71597
Observations
150
ANOVA
df
Regression
Residual
Total
1
148
149
Coefficients
Intercept
Coded Quality
8.844776
0.080224
Significance
F
0.09199 0.09199 0.0124710.911234568
1091.72137.376496
1091.8133
SS
MS
F
Standard
Upper
Lower
t Stat
P-value Lower 95%
Error
95%
95.0%
0.234624137.697649.08E-78 8.3811301329.3084228.38113
0.71838670.1116720.911235-1.33939623 1.499844-1.3394
Upper
95.0%
9.308422
1.499844
Predicted value 8.925
Last saved 9/24/2017 9:04:00 AM
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Understanding
7
/9
Good job with the hypothesis test and understanding the approach for regression. While
you came to the correct conclusion for question 3, you should have used the capability
analysis equation from lesson 13
Last saved 9/24/2017 9:02:00 AM
Critical Thinking
6
/8
Good job calculating the hypothesis test. Normally you should have used the t -test since
you are using same data. The critical value was different. Good job with regression;
however, your coefficient of X was not correct, see general comments. See below for the
capability analysis
Data
Upper tolerance limit
Lower tolerance limit
Mean (optional)
9.5
5.5
8.85
Standard deviation
2.71
Results
Mean
8.85
Upper one-sided index 0.0799508
Lower one-sided index 0.41205412
Process capability
0.0799508
index
Last saved 9/24/2017 9:04:00 AM
Key Concepts and Terms
9
/9
Good job analyzing and interpreting results from the output
Last saved 9/24/2017 9:04:00 AM
Writing
4
/4
Good job summarizing your approach and conclusions
Last saved 9/24/2017 9:04:00 AM
Scoring Summary
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Name Pengjun Zhou (PEN2159797)
Submission 1
Submitted
Status
Total Score
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Essay
1. Complete the essay using the information below.
Case Study
Background:
Land and Agua Insurance Company has a call center in Tempe, Arizona. The business
was originally established in Phoenix, Arizona in 1972 as a small business, and it has
grown with the population of the area. The insurance company specializes in bundling
insurance for cars, off-road vehicles, and watercraft (e.g., jet skis and boats). The
company has 150,000 clients in Arizona.
Marjorie Jones, Vice President of Operations, is concerned about customer complaints
and amount of time representatives are taking to resolve the calls. After studying the
issue, the company implemented improvements to operations, and a new data sample
was collected after three months. You are responsible for analyzing the results to
determine whether the improvements made a difference, and determining if the new
processes are meeting customer specifications. Additionally, you must review the data
and predict the customer call time if a defect occurs.
2. Answer the question below in essay format. Your essay must include an introduction, a
body, and a conclusion. It must address all relevant parts of each question. Your
response should be a minimum of 500 words in length, and it should include both the
appropriate statistics and support for the analysis and interpretation. Make sure to cite
any source you use. Proper citation format for a source includes the name of the
author(s), the title of the work, the date of the publication, and the page number if you
directly quote the source.
Essay Questions: New Call Time
Using the New Call Center Data, provide a summary report for the vice president including
the following information in an essay with a minimum of 500 words:
•
Using the two-sample hypothesis test comparing old call time to new call time at a .05
level of significance, discuss the hypothesis test assumptions and tests used. Provi de
the test statistic and p -value in your response. Evaluate the results of the hypothesis
test with the scenario. Provide recommendations for the vice president.
•
Using new call time and coded quality, develop a prediction equation for new call
time. Evaluate the model and discuss the coefficient of determination, significance,
and use the prediction equation to predict a call time if there is a defect.
•
Evaluate whether the new call time meets customer specification. As stated in a
previous lesson, customers indicated they did not want a call time longer than 7.5
minutes. Assume a standard deviation of 2 min is acceptable. Is the call center now
meeting the customer specifications? If not where is the specification not being met?
Explain your answers.
…
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