Statistical Analysis on Data Sets - Call Center Data Analysis

This assignment presents a comprehensive statistical analysis of two call center datasets. The student investigates the relationships between variables such as staff type (original vs. replacement), median call time, and median call time above 3 minutes. The analysis includes calculations of sample means, sample proportions, and z-scores to compare the performance of original and replacement staff. Hypothesis testing is performed to determine the significance of differences between means and proportions. Confidence intervals are constructed to estimate population parameters. The analysis culminates in a comparison of the results from both call centers, drawing conclusions about staff performance and the factors influencing customer satisfaction. The assignment covers a range of statistical techniques to provide a detailed understanding of the data and draw meaningful conclusions.

Statistical Analysis on Data Sets 1
STATISTICAL ANALYSIS ON DATA SETS
by Student’s Name
Code + Course Name
Professor’s Name
University Name
City, State
Date

Statistical Analysis on Data Sets 2
Data Analysis on Data Sets
Question one: Second Option
a) Just using the information for call Centre 1
i)
ii) Relationship of the variables
Applying difference in sample means
x1 - x2 = 33.93 – 29.54 = 4.39
It implies that the mean of complaints of “original staff” ” (4.393) is more than that of the
“replacement staff” ” for the data set in first call center.

Statistical Analysis on Data Sets 3
b) Just using the information for call Centre 2
i)
ii) Relationship between the two variables
Using descriptive statistics x1 - x2
x1 = 33.9808
x2 = 28.2426 5.7382
x1 - x2 = 5.7382
This implies that the mean complaints of the “original staff” for call center two are 5.7382 more
than the “replacement staff” .
c) Comparing a and b results
In a and b the mean of complaints that were issued against the “original staff” are more than
those issued against the “replacement staff” for the data set in call center 2.

Statistical Analysis on Data Sets 4
Question 2
a) Just using the information for call Centre 1
i)
ii) Relationship between the two variables
Applying sample proportions ( ^p1− ^p2)
Sample proportions = X
n where n is the sample size
First Proportion = 98 ÷ 155
^p1= 0.63226
Second proportion = 57 ÷ 155
^p2= 0.36774
^p1− ^p2= 0.63226 - 0.36774= 0.26452
Comment: when we consider the “median call time above 3 minutes” it is correct to conclude
that the number of calls made for complaints against the “replacement staff” are 26.452% lower

Statistical Analysis on Data Sets 5
compared to those made against the “original staff” . That is, most complaints were against
“original staff”.
b) Just using the information for call Centre 2
i)
ii) Relationship between the two variables
Applying sample proportions ( ^p1− ^p2)
Sample proportions = X
n where n is the sample size
First Proportion = 77 ÷ 116
^p1= 0.66379
Second proportion = 57 ÷ 116
^p2= 0.33621
^p1− ^p2= 0.66379 - 0.33621 = 0.32758
Comment: Therefore, if the “median call time above 3 minutes” for the second call is considered
the number of calls made to deliver complaints against the original employees are 32.758% more
than those made against the replacement workers in the data set.

Statistical Analysis on Data Sets 6
c) Comparison on a and b
The data from both call center one and two reveal that “median call time above 3 minutes” for
the calls made against the original workers are more than those made against the “replacement
staff”.
Question 3
a)
i)

Statistical Analysis on Data Sets 7
ii) Relationship of the variables
Applying difference mean of samples
x1 = 27.4
x2= 34.2323
x1 - x2 = -6.8323
The sample statistic reveals that the calls made above 3 minutes were 6.8323 more than those
made three minutes and below in call center one.
b) Just using the information for call Centre 2
i)

Statistical Analysis on Data Sets 8
ii) Relationship of the variables
Applying difference in sample means (x1 -x2 )
x1 = 27.2742

Statistical Analysis on Data Sets 9
x2= 34.4224
x1 - x2 = -7.1482
The sample statistic reveals that the calls made 3 minutes and below were 7.1482 lower than
those made above 3 minutes.
c) Comparing a and b
For both call center one and two the number of calls made above 3 minutes were higher than
those made above three minutes and below.
Question 4
Just using the call Centre 1 data set
a) Considering data for “original staff” only
Size of sample (n)
n = 125
Mean “median call time” = total “median call time” ÷ n
∑
1
n
” median call time ”÷( n)
= 423/125
= 3.384

Statistical Analysis on Data Sets 10
i) Z-score (when population mean is 3 and the standard deviation is 1.1) for sample
mean
Z-score = X - μ / σ
X = mean of population = 3
μ = mean of sample = 3.384
σ = standard deviation of sample =1.1
= (3 – 3.384) ÷ 1.1
= -0.03491
Comment: the mean of the whole population which is 3 implying that it is -0.03491 σ from the
sample mean of the “original staff”.
The mean of the population is less than the mean of the sample because the calculated z-score is
negative.
b) Considering “original staff” only
Sample size (n)
n = 115
Mean “median call time” = total “median call time” ÷ n
∑
i=1
n
median call time ÷(n)
= 340.56/115 = 2.96139
ii) Z-score (when population μ is 3 and σ is 1.1) for sample mean
Z-score = X - μ / σ

Statistical Analysis on Data Sets 11
X = mean of population = 3
μ = 2.9614
σ = 1.1
= (3 – 2.9614) ÷ 1.1
= 0.03509
Comment: the mean of the whole population which is 3 is - 0.03509 σ from the sample mean of
the “replacement staff”.
The mean of the population is more than the mean of the sample because the calculated z-score
is positive.
Question five
a) “original staff” from call center one
i) Sample size (n) = 125
ii) p̂ for “median call time > 3 minutes”
= individual events/ n
p̂ = (X÷ n)
X = 98
n = 125
p̂ = 0.784
95% confidence level of the proportion of the population
=

Statistical Analysis on Data Sets 12
= 0.784 ± 1.96. √(0.784 ( 1−0.784 ))÷125
0.784 ± 0.07214
The confidence interval at 95% is (0.85614, 0.71186)
b) For “replacement staff” only
i) n = 115
ii) p̂ with “median time call above 3 minutes”
= 57 ÷115
= 0.49565
ii) CI at 95%
= 0.49565 ± 1.96 √ 0.49565(1−0.4957)/115
0.4957 ± 0.09138
The 95% confidence interval is (0.5871, 0.40432)