Statistics for Business

This email provides answers to queries related to implementation of new system in phone business. The analysis is based on the provided data set. The email covers topics such as incoming call numbers, call survey, customer rating on Facebook, confidence in satisfaction scores and changing business mix.

Running Head: STATISTICS FOR BUSINESS
Statistics for Business
Name of the Student
Name of the University
Author note

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Dear Adam,
In this email answer are provided to the queries raised by Walter Waterson in the
email regarding implementation of new system in the phone business. The follow up is given
based on the analysis done from the provided data set in the concerned mail.
Incoming call numbers
1.The given image of automated report resembles to a box plot. The two end of such plot
indicates maximum and minimum data points in a given distribution. The minimum number
of call is 2. The number 69 represents maximum number of received calls. 46 is the first
quartile of the distribution and 61 is the third quartile. The first quartile implies of the total
call received 25 percent is less than 46. From the third quartile, it can be said less than 75
percent of received call is less than 61. The median of received call distribution is 52
implying half of the received calls in a day are less than 52.
2. A distribution is left skewed it tails extends towards left more than its right tail. From the
above image, the received call has a widely extended tail to the left. Therefore, Walter has
rightly identified that the distribution is negatively skewed or left skewed. This implies
average number of phone call received lies to the left of median number of phone call.
Number of call less than median number are highly scattered while those greater than median
are close to each other.
3. From the plotted image of the phone calls the least number of received call is 2. However,
is has observed that even in the quietest day minimum 35 calls are received. Several factors
can cause this discrepancy. Interruption in the telephone network can be one reason to reach
the lowest number of 2 phone calls. Sometime company intentionally keeps all the telephone
lines close because of system upgradation. Network traffic or technical glitches likely to
make telephone line unreachable at a time results in lower number of calls.

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4. In a distribution outlier is an observation that is most unlikely to other observation in the
dataset. In terms of statistics, an observation is identified as outlier if is 1.5 times below the
first quartile and 1.5 times above third quartile. The former is known as lower range of outlier
while the latter is known as upper range of outlier. From the data given in the call number
sheet, the first and third quartile is estimated as 44 and 66 respectively. Consequently, the
upper and lower outlier range is 84 and 20. There are only two days having number of calls
outside this range. 2 days have call less than 20 while no observation is found above 84.
Therefore, 2 is an outlier.
Call Survey
5. From the call survey sheet indicating satisfaction scores of 100 customers on a scales
ranging from 1 to 5 the mean satisfaction score is 3.88 and associated standard deviation is
1.22.
6. The following chart shows comparison of average satisfaction rating for each type of job
Emergency Improvements Maintenance
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Comaprison of Average rating based on
type of Job
Job Type
Average Rating
7. The jobs are classified into three categories- Emergency, improvement and maintenance.
27 responses are received for emergency. For improvement and maintenance types responses
received are 37 and 36 respectively.

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The data given on phone call type is categorical. For non-numeric data, the average
cannot be computed. However, the survey responses indicate most of the telephone services
are for improvement and maintenance. For job type of emergency less number of calls are
received than improved and maintenance type.
8. The average call times as obtained from the chart is 4.99 minutes and the corresponding
standard deviation of call times is 2.32 minutes.
9. The calculated mean for recent sample calls is 4.50 minutes and that of the standard
deviation is 1.07 minutes.
10. There is negligible difference in average call times between 2017 and 2015. The call
times in 2017 is lowered by (4.99 – 4.50) = 0.49 minutes. However, the variability of call
times indicated by the standard deviation is less in 2017 as compared to 2015. The reason
behind less volatility in call times may be efficient implementation of technology to solve
problem in telephone network. This helps to keep average call duration in the two years in
balance.
Customer Rating on Facebook
11. From the given contingency table showing customer ratings it is observed that out of 100
callers 35 callers have given a give star rating. Therefore, the probability that a five-star
rating is obtained is (35/100) = 0.35.
12. The jobs classified as improvement received less than 4 star from 21 customers. Hence,
probability that ‘improvement’ will be rated as 4 star is (21/100) = 0.21.
13. The customer ratings can be used for business promotion. As shown from the table jobs
classified as emergency and maintenance mostly received four or five-star ratings. However,
for “improvement” there are 21 customers giving less than four-star to the services.

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Therefore, exclusion of ratings for improvement will produce a higher average rating. The
higher average rating will help the business to attract more customers. From the given table,
the average rating when only emergency and maintenance is taken for consideration is 4.38.
Confidence in Satisfaction Scores
14. The rating of customer have been gathered from customer’s responses received in three
days. In reality, however the number of customers are not limited by three days only. The
ratings derive from the entire population of customers may differ a lot from that obtained
from the sample. The computation of confidence interval at 5% level of significance implies
there are 95% chances that average rating of different job types is within 4.
15. The reliable difference in satisfaction score between job types can be analyzed from
single factor ANOVA test. The null hypothesis here is there is no significant difference in
satisfaction scores between different job types. The significance level of 0.05. The
corresponding p value is less than 0.05. This implies rejection of null hypothesis. In other
words, there is 95% possibility of having a significant difference in satisfaction score for
different job types.
16. The ANOVA result significant difference in satisfaction scores can be further confirmed
by independent two sample t test sample t test with equal variances. 3 different tests are
performed for testing difference in mean score taking any two job types at a time. The three
results indicate a significant difference of mean satisfaction scores across different groups. In
each cases the probability value is less than 5% level of significance and hence, ensure 95%
confidence regarding the results obtained.
Changing Business Mix
17. In order to examine whether investment return on emergency job type is lower than that
for improvement independent two sample t test needs to be performed. From the test result, it

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is seen that critical t value is greater than computed t value implying no significant difference
of investment return between the two group. As the test is conducted taking alpha equal 95, it
can be said that the obtained result holds for 95% cases.
18. The null hypothesis is “there is no significant difference in ROI between two job types
Emergencies and Improvement”. The analysis done above shows acceptance of the null
hypothesis.
19. If the sample data shows a difference in ROI between Emergency and Improvement job
types, then the statistical test contains an error. The probability of occurring such error is (1-
0.05) = 0.95. This type of error is known as type II error.
20. The satisfaction rating for Emergency job type is mostly five-star or four star. However,
for Improvement only 16 customers rated the service as five star or four star while 21
customers has given a rate less than 4. However, the statistical test shows there is no
significant difference for return on investment between Emergency and Improvement job
types. Based on customer rating is can be said that the business should give focus on
improving it service on “Improvement” service. Otherwise lower rating in this job type would
reduce the overall business rating. With improvement in this type of Job the return can also
be improved. Other thing the company can do is to close “Improvement” job type and focus
only on emergency type.
Hope, the all question of Mr. Walter has been addressed resolving the problems
related to the business.
Regards,
Name of the Student

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Student number