# computer test questions

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```					                                       Solutions to Trial computer test questions

The following problems are similar to what you might expect in the computer test/exam. The data is contained
in a Minitab worksheet entitled data for trial computer test questions.

1.

a. Comparison of service quality measurements between females and males

Dotplot of Service quality

1

2

8               10            12           14       16        18
Service quality

Panel variable: Gender

The females (gender =1) appear to have slightly higher levels of their perceptions of service quality than
the males . The following are the summary statistics :

Descriptive Statistics: Service quality

Variable             Gender         N     N*      Mean        SE Mean      StDev   Minimum       Q1
Service quality      1             20      0    14.300          0.612      2.736     7.000   13.000
2             20      0    13.100          0.429      1.917     9.000   12.000

Variable             Gender        Median           Q3        Maximum
Service quality      1             15.000       16.750         18.000
2             13.000       14.750         16.000
The average service quality level is 14.3 amongst the female group compared with 13.1 in the male
group. We use an independent two sample t-test to test the statistical significance :
Two-sample T for Service quality

Gender    N    Mean     StDev       SE Mean
1        20   14.30      2.74          0.61
2        20   13.10      1.92          0.43

Difference = mu (1) - mu (2)
Estimate for difference: 1.200
95% CI for difference: (-0.318, 2.718)
T-Test of difference = 0 (vs not =): T-Value = 1.61                            P-Value = 0.117    DF = 34

The p value of 0.117 indicates that this difference is not statistically significant.
Comparison of loyalty measurements between females and males

Dotplot of Loyalty

1

2

8            10        12          14         16        18
Loyalty

Panel variable: Gender

The females (gender =1) appear to have higher levels of loyalty than the males. The following are the
summary statistics

Descriptive Statistics: Loyalty

Variable   Gender      N   N*       Mean        SE Mean   StDev       Minimum        Q1    Median
Loyalty    1          20    0     14.700          0.493   2.203         9.000    14.000    15.000
2          20    0     12.850          0.582   2.601         8.000    11.000    13.000

Variable   Gender         Q3      Maximum
Loyalty    1          16.000       19.000
2          15.000       17.000
The average loyalty score for the females is 14.7 compared with 12.85 for the males. We test the
statistical significance of this using the two sample t-test.
Two-sample T for Loyalty

Gender    N    Mean    StDev      SE Mean
1        20   14.70     2.20         0.49
2        20   12.85     2.60         0.58

Difference = mu (1) - mu (2)
Estimate for difference: 1.850
95% CI for difference: (0.304, 3.396)
T-Test of difference = 0 (vs not =): T-Value = 2.43                     P-Value = 0.020       DF = 36

The p-value of 0.02 indicates that there is statistically significant evidence of a difference in the average
loyalty between females and males.

The relationship between service quality and loyalty

For the females the following is the plot of the relationship between service quality and loyalty
Scatterplot of Loyalty vs Service quality
20

18

16

Loyalty
14

12

10

6        8        10          12           14     16        18
Service quality

There appears to be a relationship between service quality and loyalty amongst the females. This is
confirmed by the correlation between the two variables which is 0.872 (p value = 0.00)

For the males the following is the plot

Scatterplot of Loyalty vs Service quality

17

16

15

14

13
Loyalty

12

11

10

9

8

9   10       11         12        13       14   15     16
Service quality

There doesn’t appear to be much of a relationship between loyalty and service quality for the males.
This is confirmed by correlation which is 0.13 (p=0.585)

b.     Summary

Data was collected on 20 female and 20 male subjects on measurements in a study of customer loyalty
and perceptions of service quality. The study was designed to investigate differences between males and
females on loyalty and perceptions of customer service. There is also an interest in understanding the
link between perceptions of service quality and loyalty.

The female subjects showed generally higher responses on their perceptions of service quality (average
= 14.3 compared with an average of 13.0 for the males). Statistical analysis showed that this difference
was not statistically significant.

The following graph of the customer loyalty measure on each group highlights a higher level of loyalty
in the female group (average = 14.7 compared with an average of 12.85 for the males).
Dotplot of Loyalty

1

2

8         10        12         14                  16            18
Loyalty

Panel variable: Gender

This result was statistically significant (p= 0.02) and is an important observation for the company.

In order to investigate the relationship between service quality and loyalty the following graphs show
this relationship for the females and males separately.

Scatterplot of Loyalty vs Service quality                                                     Scatterplot of Loyalty vs Service quality
20
17

16
18
15

16                                                                                       14
Loyalty

13
Loyalty

14
12

11
12
10

10                                                                                       9

8

6   8         10         12               14    16   18                                       9   10        11     12        13     14        15   16
Service quality                                                                               Service quality

It is clear that the relationship between service quality and loyalty is quite different between females and
males. There is a relationship between the two variables for the females but not for the males. For the
females the correlation is 0.87 (p=0.00) whilst for the males it is 0.13 (p=0.585)

In conclusion the company should note that the females have higher loyalty levels than the males and
that for the females there is a significant relationship between perceptions of service quality and loyalty.
This is not the case with the males. Improving service quality may have a positive impact on female
loyalty but not for males. Further investigation is required to understand the drives of loyalty for males.

2. We are taking prices from the two suppliers on the same item. The responses are therefore paired (or
related). We need to calculate the differences and plot them on a dotplot. I have calculated supplier 1 –
supplier 2
Dotplot of difference

-0.48        -0.32    -0.16          0.00      0.16     0.32           0.48
difference

There doesn’t appear to be much evidence of a difference between the supplier prices, the points are
reasonably well spread about 0. We use a one sample t-test on the differences : the output is shown
below.

One-Sample T: difference

Test of mu = 0 vs not = 0

Variable      N    Mean    StDev         SE Mean           95% CI                    T               P
difference   10   0.033    0.324           0.102      (-0.199, 0.265)             0.32           0.755

The p-value of 0.755 shows that there is no statistically significant evidence of a difference between the
supplier prices.

The main assumption is the normality of the differences which is reasonable according to the following
normal plot (p>0.1)

Probability Plot of difference
Normal
99
Mean       0.033
StDev     0.3241
95                                                            N             10
RJ         0.983
90
P-Value   >0.100
80
70
Percent

60
50
40
30
20

10

5

1
-0.5            0.0             0.5             1.0
difference
3. Using the multiple regression process we include the three predictor variables to get the following
output :

The regression equation is

Hotel expediture = 2.55 + 0.0105 average room rate + 1.01 Number of visitors

- 4.05 TPI

Predictor          Coef       SE Coef                         T                       P

Constant          2.552          7.112                     0.36             0.727

average        0.010492      0.002529                      4.15             0.002

Number o         1.0103        0.4300                      2.35             0.039

TPI              -4.048          3.068                -1.32                 0.214

S = 1.388         R-Sq = 93.5%                 R-Sq(adj) = 91.7%

The output suggests that the variable TPI does not have any significant impact beyond the other two
variables in the model. The following is the output obtained by leaving this variable out
The regression equation is

Hotel expediture = - 6.05 + 0.0109 average room rate + 1.55 Number of visitors

Predictor          Coef       SE Coef                         T                       P

Constant         -6.052         2.926                 -2.07                 0.061

average        0.010887     0.002587                       4.21             0.001

Number o         1.5517        0.1323                 11.73                 0.000

S = 1.430         R-Sq = 92.4%                 R-Sq(adj) = 91.2%

This model gives a good r-sq. The following plot of the residuals vs the fitted values shows some
evidence of a curved relationship between the residuals and the fitted values.

Residuals Versus the Fitted Values
(response is Hotel ex)

2

1
Residual

0

-1

-2

-3
10             15               20   25
Fitted Value

The plot of the fitted values vs the two variables in the model are as follows
Number of visitors

Residuals Versus Number o
(response is Hotel ex)

2

1

Residual
0

-1

-2

-3
2   3     4     5       6      7       8   9      10   11      12
Number o

Average room rate

Residuals Versus average
(response is Hotel ex)

2

1
Residual

0

-1

-2

-3
800         900         1000           1100        1200         1300
average

We may get a slightly better model by including a quadratic term in the number of visitors. When we do
this (by calculating a new variable which is the square of the number of visitors) we see the following
output :
The regression equation is

Hotel expediture = - 9.27 + 0.0101 average room rate + 2.93 Number of visitors

- 0.0987 numb of visitors sq

Predictor            Coef     SE Coef                                             T                      P

Constant         -9.271          3.067                                  -3.02                    0.012

average        0.010131      0.002342                                       4.32                 0.001

Number o         2.9255         0.6944                                      4.21                 0.001

numb of        -0.09872       0.04917                                   -2.01                    0.070

S = 1.278          R-Sq = 94.5%                           R-Sq(adj) = 93.0%

The p value on the last line is 0.070 indicating that the square of the visitors is almost significant as an
extra variable but not quite. We would probably leave the model at its previous stage i.e.

The regression equation is

Hotel expediture = - 6.05 + 0.0109 average room rate + 1.55 Number of visitors
4. The following is a dotplot of the comparison between the two menus using gross weekly sales.

Dotplot of gross weekly sales

1

2

4.0         4.2         4.4      4.6      4.8            5.0         5.2         5.4
gross weekly sales

Menu B appears to be generally achieving higher sales than Menu A. To test the statistical significance
of this we use a two sample t-test
Two-sample T for gross weekly sales

menu    N    Mean   StDev             SE Mean
1      12   4.417   0.279               0.081
2      12   4.725   0.314               0.091

Difference = mu (1) - mu (2)
Estimate for difference: -0.308
95% CI for difference: (-0.560, -0.056)
T-Test of difference = 0 (vs not =): T-Value = -2.54                                           P-Value = 0.019                       DF = 21

The p value of 0.019 indicates statistically significant evidence of a difference in the sales from the two
menus. The second menu has a higher mean sales (\$4,725) compared to \$4,417 for the first menu. The
main assumption here is that the individual samples are normally distributed. By splitting the file I
obtained the following normality plots :

Probability Plot of gross weekly sales
Normal
99
Mean       4.417
StDev     0.2791
95                                                                                          N             12
RJ         0.986
90
P-Value   >0.100
80
70
Percent

60
50
40
30
20

10

5

1
3.6         3.8         4.0   4.2    4.4     4.6         4.8         5.0         5.2
gross weekly sales
Probability Plot of gross weekly sales
Normal
99
Mean       4.725
StDev     0.3137
95                                                               N             12
RJ         0.970
90
P-Value   >0.100
80
70

Percent
60
50
40
30
20

10

5

1
4.0   4.2     4.4     4.6   4.8     5.0   5.2   5.4   5.6
gross weekly sales

In both cases the assumption of normality is ok because the p values are > 0.05.(in fact they are >0.1 in
both cases).

5.

a. Using normdist we can calculate that approximately 6.7% of invoices result in a loss of <\$20

b. Approximately 93.3% of invoices have errors that are more than \$20 i.e. 933 out of 1000, the
total cost would be \$9330.

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