Statistics for Business

This report provides an analysis of phone call data, customer satisfaction ratings, and job types for a business. The report includes insights on outliers, skewness, and probability. ANOVA and t-tests are used to analyze return on investment for different job types.

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

1STATISTICS FOR BUSINESS
Dear Adam,
With reference to the email sent by Walter Waterson regarding his new implementation of the
phone business, the following questions have been answered. The analysis conducted to
answer his questions is mainly based on the dataset provided by him.
1. There has been implementation of a new phone system in their business which will
automatically record the data on all the incoming calls on the telephone. The values 2
and 69 given in the image indicates the minimum and the maximum number of calls
respectively received by the company in a day. 46 and 61 are respectively the first and
the third quartiles of the data on the number of calls. 46 indicates that 25 percent of
the calls received in a day are less than 46 and 25 percent of the received in a day are
more than 61. 52 indicates than 50 percent of the calls received in a day are less than
52. This is known as the median.
2. It is correctly understood by Walter that the plot given above shows that the
distribution of the number of phone calls in a day in actually left skewed (negatively
skewed). This indicates that the number of phone calls above the median number of
phone calls (48) are widely scattered whereas the number of phone calls less than 48
are close to 48.
3. It has been observed that the minimum number of calls in a day was 2 calls but
mostly, on an average the minimum number of calls received in a day was 35. There
can be several reasons for receiving 2 calls in a day. There can be network error
which made people unable to reach to the company. Thus they received less number
of calls. There can also be some system upgrades for which the company shut down
their telephone lines. This can also result in the lesser number of calls received by the
company.

2STATISTICS FOR BUSINESS
4. From the box plot generated, it can be said that 2 is an outlier. There are no other
existing outliers in the dataset. A data point is called an outlier if it lies 1.5 times of
the interquartile range above the third quartile and 1.5 times of the interquartile range
below the first quartile. These two ranges are known as the upper and the lower
outlier range.
In this data, the first quartile is 44 and the third quartile is 60. Thus, the interquartile
range is 16. Therefore, the upper outlier range is (60 + 1.5 * 16) = 84 and the lower
outlier range is (44 – 1.5 * 16) = 20. There were two days when the number of phone
calls received is less than 20. In one day, only two calls were received and on the
other day, the number of calls received was 3. More than 84 calls were not received
on any day.
5. From the ratings given by the customers on their satisfaction with the services of the
company, it has been observed that the average rating given by the selected 100
customers is 3.88 which is considerably high on a scale of 1 – 5. The standard
deviation of the ratings has been found to be 1.22.
6. The chart showing the average satisfaction rating for each of the job type is given
below:
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

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7. It can be observed from the analysis of the responses of the 100 callers that the
number of people that have the emergency service from the company is 27, the
number of people that called in for improvements are 37 and the number of people
that called for maintenance is 36.
It is not possible to find the average type of calls as the type of phone calls is
not numerical. But it can be said that people mostly call the company for services
related to maintenance and improvements. Lesser emergency calls are received in
comparison to the other two call types.
8. From the given chart, the approximate mean duration of calls has been found to be
4.99 minutes with a standard deviation of 2.32 minutes.
9. The data on call duration was started to be captured in the last few days. It has been
observed from the data on call duration that the average time people talk on the phone
with the company is 4.50 minutes with a standard deviation of 1.07 minutes.
10. It can be seen that there has not been much difference in the duration of calls from
2015, though the standard deviation of the call duration has decreased in 2017.
Moreover, it can be said that the duration of calls has decreased in 2017. One reason
behind this can be such that the company has been more efficient in solving the
problems over the phone. Thus the call durations were all close to the average
duration in 2017 than in 2015.
11. From the data summary given in the contingency table, it can be seen that the number
of people that has given a five-star rating is 35 out of 100 chosen callers. Thus, the
probability of receiving a five-star rating is 0.35.
12. From the contingency table, it can also be seen that the number of callers who have
given ratings less than four-star on jobs classified as “improvements” is 21. Thus, the

4STATISTICS FOR BUSINESS
probability of getting a rating less than 4 star on the job classified as “improvement”
is 0.21.
13. Walter wants to attach the average of the facebook ratings for advertisement. The
average ratings for maintenance and emergency will be considered for it. Ratings for
improvements will not be considered. Thus, the average facebook rating to be
displayed for the advertisement is 4.38.
14. The customer ratings that has been collected are on the basis of the responses of the
callers of only three days. Originally, there are a lot of more customers. The ratings
might be a lot different from what has been received by the three day customer
satisfaction. By conducting respective analyses, it can be said with 95 percent
confidence that the average rating given by the callers on facebook is not less than 4.
15. ANOVA test has been conducted to test the existence of any reliable difference in the
satisfaction scores between different job types. From the results of the ANOVA test, it
can be said with 95% confidence that there is significant difference between the
satisfaction scores of the callers of different job types as the p-value is less than 0.05
(the level of significance).
16. On the basis of the last question, independent sample t-test has been conducted
considering two job types at one time and comparing their mean satisfaction scores. It
can be seen from the results of the three different t-tests that there is significant
difference between the satisfaction scores for each of the job types with the other two
as the p-value is less than 0.05 (the level of significance) for all the tests. This can be
claimed with 95 percent confidence.
17. The improvement job has been difficult for the company. Thus, they decided to stop
the improvement plumbing work and focus on the emergency work and the improve
the business in that sector. It has been observed from the results of the t test that the p-

5STATISTICS FOR BUSINESS
value (0.182) is greater than the level of significance (0.05). Thus, there is no
significant difference in the return on investment for the two different job types. This
can be claimed with 95 percent confidence.
18. The null hypothesis for answering the above problem was “No significant difference
exists between the return on investments (ROI) on the two different job types
improvements and emergencies”. The above analysis shows that the null hypothesis
has been accepted.
19. If the statistical test shows that there is difference between the ROI of improvements
and emergencies, there is an error in the analysis. The probability of that error is 0.05.
This type of error when the null hypothesis is rejected when it is true is known as type
one error.
20. It has been observed from all the analysis that there is no significant difference
between the return on investments of the two different job types, emergencies and
improvements but the overall satisfaction scores of the customers are much higher for
the emergency type of business than the improvement type of business. Thus, the
improvement business has to be made better in order to satisfy the customers.
Otherwise, it will be better to switch to the emergency business and shut down the
improvement business from the company side. This is more likely to increase the
customer satisfaction.
Hopefully, answers to all the questions that Mr. Walter was having problems with has
been answered.
Kind regards,
Name of the student
Student Number