Business statistics

Question 1
OPTION 1
a) call centre 1
i)
    Row Labels
    Count of Median call time?
    Average of Median call time?3
    StdDev of Median call time?2
    original
    98
    3.37
    0.36
    replacement
    119
    2.86
    0.35
    Grand Total
    217
    3.09
    0.43
The median call time by original staff is greater than replacement staff. The total number of calls by original staff is less than replacement staff.
ii)
The median call time for original staff is greater than the median call time for of replacement staff .
b) call centre 2
i)
    Row Labels
    Count of Median call time?
    Average of Median call time?3
    StdDev of Median call time?2
    original
    108
    3.39
    0.39
    replacement
    109
    2.78
    0.31
    Grand Total
    217
    3.08
    0.46
The median call time by original staff is greater than replacement staff. The total number of calls by original staff is equal to that by replacement staff.
ii)
The median call time for original staff is greater than the median call time for of replacement staff .
c)
In call centres 1 and 2, the median call time by original staff is greater than replacement staff.
Question 2
a) call centre 1
i)
    Count of Original staff or replacement staff?
    Column Labels
    
    
    Row Labels
    no
    yes
    Grand Total
    original
    21
    77
    98
    replacement
    76
    43
    119
    Grand Total
    97
    120
    217
Most calls were either operated by original staff with median call time above 3 minutes or were operated by replacement staff with median call time less than 3 minutes. There are very calls by original staff who have median below 3 minutes as well as replacement staff who have median above 3 minutes.
ii)
    Count of Original staff or replacement staff?
    Column Labels
    
    
    Row Labels
    no
    yes
    Grand Total
    original
    9.68%
    35.48%
    45.16%
    replacement
    35.02%
    19.82%
    54.84%
    Grand Total
    44.70%
    55.30%
    100.00%
There are 36% calls were either operated by original staff with median call time above 3 minutes or were operated by replacement staff with median call time less than 3 minutes. There are only 10% calls operated by original staff with median call time below 3 minutes. There are 20% calls operated by replacement staff who have median above 3 minutes.
b) call centre 2
i)
    
    
    
    
    Count of median above 3 minutes?
    Column Labels
    
    
    Row Labels
    no
    yes
    Grand Total
    original
    25
    83
    108
    replacement
    82
    27
    109
    Grand Total
    107
    110
    217
Most calls were either operated by original staff with median call time above 3 minutes or were operated by replacement staff with median call time less than 3 minutes. There are very calls by original staff who have median below 3 minutes as well as replacement staff who have median above 3 minutes.
ii)
    Count of median above 3 minutes?
    Column Labels
    
    
    Row Labels
    no
    yes
    Grand Total
    original
    11.52%
    38.25%
    49.77%
    replacement
    37.79%
    12.44%
    50.23%
    Grand Total
    49.31%
    50.69%
    100.00%
In call centre 2, there are 35% original staff who has median above 3 minutes. In call centre 2, there are 35% replacement staff who has median below 3 minutes. There are 11% original staff who have median below 3 minutes. There are 18% replacement staff who have median above 3 minutes.
c) Compare the results in parts (a) and (b)
In both the call centres, most calls were either operated by original staff with median call time above 3 minutes or were operated by replacement staff with median call time less than 3 minutes. There are very calls by original staff who have median below 3 minutes as well as replacement staff who have median above 3 minutes.
Question 3
a) call centre 1
i)
    r =
    0.909
Since all points show an upward trend and are plotted close to each other, there is a strong positive linear relationship between median call time and number of complaints.
ii)
There is a strong positive linear relationship between median call time and number of complaints. With the increase in value of median call time, the value of number of complaints also increases drastically.
b) call centre 2
i)
    r =
    0.8754
Since all points show an upward trend and are plotted close to each other, there is a strong positive linear relationship between median call time and number of complaints.
ii)
There is a strong positive linear relationship between median call time and number of complaints. With the increase in value of median call time, the value of number of complaints also increases drastically.
c)
For both the call centres, With the increase in value of median call time, the value of number of complaints also increases drastically.
Question 4
call centre 1
    Row Labels
    Count of Median call time?
    Average of Median call time?3
    original
    98
    3.37
    replacement
    119
    2.86
    Grand Total
    217
    3.09
a) original staff
i) What is sample size and sample mean of median call time
n= 98
Xbar=3.37
ii) what is the z score of sample mean if population mean is 3 and population standard deviation is 1.1
Z score = (X-mean)/sd
Z score = (3.37-3)/1.1 = 0.336
b) replacement staff
i) What is sample size and sample mean of median call time
n= 119
Xbar= 2.86
ii) what is the zscore of sample mean if population mean is 3 and population standard deviation is 1.1
Z score = (X-mean)/sd
Z score = (2.86-3)/1.1 =...