The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The variables in the survey can be found in the file CODING. In this section, hypothesis testing will be used to examine the significance of some of the survey results. From a managerial perspective, the information gained from this database exercise would be useful in determining whether the mean attitude toward a given area differed significantly from the “neutral” level, in observing and comparing the mean attitude scores exhibited toward the three shopping areas, and in examining the strengths and weaknesses of a manager’s shopping area relative to the other two areas. If such a study were repeated from time to time, management could observe the extent to which the overall attitude toward their shopping area was becoming stronger or weaker in the eyes of the consumer, thus helping them select business strategies that could retain and take advantage of their area’s strengths and either correct or minimize the effect of its weaknesses. 1.Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent’s general attitude toward each of the three shopping areas. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement. a. Calculate the mean attitude score toward the Springdale Mall shopping area and compute the sample standard deviation. Does this area seem to be well regarded by the respondents? The mean attitude score toward the Springdale Mall is 3.6467. This mean value puts the attitude toward Springdale Mall just over midway between “Neutral” and “Like”, so it would be a stretch to consider this mall to be “well regarded”. The rating is actually somewhat better than “indifferent”. b. In a two-tail test at the 0.10 level, compare the sample mean calculated in part (a) to the 3.0 “neutral” value. Use the null hypothesis and the alternative hypothesis . The hypotheses are: Null: Alternative: The critical values for a two-tailed test at α = 0.10 are ±1.645. The test statistic is 6.5436. Since the test statistic is greater than the positive critical value, the decision is to reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance to support a claim that the population mean attitude toward Springdale Mall is different from 3.0. c. Generate the 90% confidence interval for the population mean and use this interval in verifying the conclusion obtained in part .

1. The major shopping areas in the community of Springdale
include Springdale Mall, West Mall, and the downtown area on
Main Street. A telephone survey has been conducted to identify
strengths and weaknesses of these areas and to find out how
they fit into the shopping activities of local residents. The 150
respondents were also asked to provide information about
themselves and their shopping habits. The data are provided in
the file SHOPPING. The variables in the survey can be found in
the file CODING.
In this section, hypothesis testing will be used to examine the
significance of some of the survey results. From a managerial
perspective, the information gained from this database exercise
would be useful in determining whether the mean attitude
toward a given area differed significantly from the “neutral”
level, in observing and comparing the mean attitude scores
exhibited toward the three shopping areas, and in examining the
strengths and weaknesses of a manager’s shopping area relative
to the other two areas. If such a study were repeated from time
to time, management could observe the extent to which the
overall attitude toward their shopping area was becoming
stronger or weaker in the eyes of the consumer, thus helping
them select business strategies that could retain and take
advantage of their area’s strengths and either correct or
minimize the effect of its weaknesses.
1.Item C in the description of the data collection instrument
lists variables 7, 8, and 9, which represent the respondent’s
general attitude toward each of the three shopping areas. Each
of these variables has numerically equal distances between the
possible responses, and for purposes of analysis they may be
considered to be of the interval scale of measurement.
a. Calculate the mean attitude score toward the Springdale Mall

2. shopping area and compute the sample standard deviation. Does
this area seem to be well regarded by the respondents?
The mean attitude score toward the Springdale Mall is
3.6467.
This mean value puts the attitude toward Springdale Mall
just over midway between “Neutral” and “Like”, so it would
be a stretch to consider this mall to be “well regarded”. The
rating is actually somewhat better than “indifferent”.
b. In a two-tail test at the 0.10 level, compare the sample mean
calculated in part (a) to the 3.0 “neutral” value. Use the null
hypothesis and the alternative hypothesis .
The hypotheses are:
Null:
Alternative:
The critical values for a two-tailed test at α = 0.10 are
±1.645.
The test statistic is 6.5436.
Since the test statistic is greater than the positive critical
value, the decision is to reject the null hypothesis.
There is sufficient evidence at the 0.10 level of

3. significance to support a claim that the population mean
attitude toward Springdale Mall is different from 3.0.
c. Generate the 90% confidence interval for the population mean
and use this interval in verifying the conclusion obtained in part
(b).
The 90% confidence interval for the population mean is
(3.4841, 3.8092).
Since the 90% confidence interval does not include the
value 3.0, a claim that the population mean attitude toward
Springdale Mall is different than 3.0 is
supported.
d. What is the p-value associated with the hypothesis test?
The p-value is 0.0000.
e. Repeat parts (a) through (d) for the Downtown shopping area.
The mean attitude score toward the Downtown shopping
area is 3.3933.
This mean value puts the attitude toward Downtown
shopping area just over the “Neutral” level. While the
attitude is positive, it is not necessarily sufficiently
different from the “neutral” level to be considered “well
regarded”.
The hypotheses are:
Null:

4. Alternative:
The critical values for a two-tailed test at α = 0.10 are
±1.645.
The test statistic is 4.3612.
Since the test statistic is greater than the positive critical
value, the decision is to reject the null hypothesis.
There is sufficient evidence at the 0.10 level of
significance to support a claim that the population mean
attitude toward the Downtown shopping area is different
from 3.0.
The 90% confidence interval for the population mean is
(3.2450, 3.5417).
Since the 90% confidence interval does not include the
value 3.0, a claim that the population mean attitude toward
the Downtown shopping area is different than
3.0 is supported.
The p-value is 0.0000.
f. Repeat parts (a) through (d) for the West Mall shopping area.
The mean attitude score toward the West Mall shopping
area is 3.2333.
This mean value puts the attitude toward West Mall
shopping area just over the “Neutral” level. While the

5. attitude is positive, it is not necessarily sufficiently
different from the “neutral” level to be considered “well
regarded”.
The hypotheses are:
Null:
Alternative:
The critical values for a two-tailed test at α = 0.10 are
±1.645.
The test statistic is 2.4373.
Since the test statistic is greater than the positive critical
value, the decision is to reject the null hypothesis.
There is sufficient evidence at the 0.10 level of
significance to support a claim that the population mean
attitude toward the West Mall shopping area is different
from 3.0.
The 90% confidence interval for the population mean is
(3.0759, 3.3908).
Since the 90% confidence interval does not include the
value 3.0, a claim that the population mean attitude toward
the West Mall shopping area is different than
3.0 is supported.

6. The p-value is 0.0148.
2.If Springdale Mall offered exactly the same benefits as the
other two shopping areas, we would expect exactly one-third of
those who expressed an opinion to select it as the area best
fitting the description for variable number 10 (“Easy to
return/exchange goods”). In testing whether Springdale Mall
differs significantly from this expected proportion, the null and
alternative hypotheses will be . Carry out the following analyses
for Springdale Mall:
a. Analyzing the data for variable 10, use the preceding null and
alternative hypotheses in testing the null hypothesis at the 0.05
level.
After removing all of the “4” responses (“4” = “No
Opinion”), there are a total of 117 responses, and 60 that
indicate a preference for Springdale Mall.
The sample proportion is:
The hypotheses are:
Null:

7. Alternative:
The critical values for a two-tailed test with α = 0.05 are
±1.96.
The test statistic is:
Since the test statistic is greater than the positive critical
value, the decision is to
reject the null hypothesis.
There is sufficient evidence at the 0.05 level of
significance to support a claim that the proportion who
prefer the Springdale Mall differs from 0.33.
b. Determine the p-value for the test conducted in part (a).
The p-value for this test is 0.0000.
c. Repeat parts (a) and (b) for variables 11–17.
For the remaining variables, the hypotheses and critical
values remain the same.
The tests and the corresponding results are:
Variable 11 (High quality of goods):
Test statistic value: 6.3056

8. Decision: Reject the null hypothesis
Conclusion: The proportion who prefer
Springdale Mall in this category
differs from 0.33.
Variable 12 (Low Prices)
Test statistic value: -3.1523
Decision: Reject the null hypothesis
Conclusion: The proportion who prefer
Springdale Mall in this category
differs from 0.33.
Variable 13 (Good variety of sizes/styles)
Test statistic value: 9.9551
Decision: Reject the null hypothesis
Conclusion: The proportion who prefer
Springdale Mall in this category
differs from 0.33.
Variable 14 (Sales staff helpful/friendly)
Test statistic value: 5.0786
Decision: Reject the null hypothesis
Conclusion: The proportion who prefer
Springdale Mall in this category
differs from 0.33.

9. Variable 15 (Convenient shopping hours)
Test statistic value: 7.6580
Decision: Reject the null hypothesis
Conclusion: The proportion who prefer
Springdale Mall in this category
differs from 0.33.
Variable 16 (Clean stores and surroundings)
Test statistic value: 10.2075
Decision: Reject the null hypothesis
Conclusion: The proportion who prefer
Springdale Mall in this category
differs from 0.33.
Variable 17 (A lot of bargain sales)
Test statistic value: 0.7792
Decision: Fail to reject the null hypothesis
Conclusion: The proportion who prefer
Springdale Mall in this category is
not different from 0.33.
d. Based on the preceding analyses, identify the principal
strengths and weaknesses exhibited by Springdale Mall.
The analysis shows that Springdale Mall is doing well compared
to the other malls in all categories except for Variable 12 (“Low
Prices”) and Variable 17 (“A lot of bargain sales).

10. In the case of the “low prices” category, the hypothesis test
shows that the proportion who selected Springdale Mall for this
category is different from 0.33, but the negative test statistic
value (-3.1523) indicates that Springdale is not doing well in
this particular category, as their proportion of votes is well
below 0.33.
In the case of the “bargain sales” category, the hypothesis test
shows that the proportion who preferred Springdale Mall in this
category is not significantly different from 0.33. This may mean
that Springdale Mall is doing just as well as the other malls in
this category, and may represent an opportunity for the mall to
distance itself from its competitors. Of course, depending on the
type of stores in the mall, being known for “bargain sales” may
not fit with the mall’s overall image.
In all of the other categories, Springdale Mall’s proportion of
votes exceeded 0.33, and the test statistic was positive,
indicating that Springdale Mall outperformed its competitors in
these categories.
p̂ =
x
n
=
60
117
= 0.5128
ˆ
p=
x
n

11. =
60
117
=0.5128
H0 : p = 0.33
H
0
:p=0.33
H1 : p ≠ 0.33
H
1
:p¹0.33
z =
x − np
p 1− p( )n
z =
60− 117( ) 0.33( )
0.33( ) 1− 0.33( ) 117( )
z = 4.2056
z=
x-np
p1-p
()
n
z=

12. 60-117
()
0.33
()
0.33
()
1-0.33
()
117
()
z=4.2056
H0 :µ = 3.0
H
0
:µ=3.0
H1 :µ ≠ 3.0
H
1
:µ¹3.0
The major shopping areas in the community of Springdale
include Springdale Mall, West Mall,
and the downtown area on Main Street. A telephone survey has
been conducted to identify
strengths and weaknesses of these areas and to find out how
they fit into the shopping activities

13. of local residents. The 150 respondents were also asked to
provide information about themselves
and their shopping habits. The data are provided in the file
Shopping (attached below). The
variables in the survey can be found in the file Coding (attached
below).
In this exercise, some of the estimation techniques presented in
the module will be applied to the
Springfield Shopping survey results. You may assume that these
respondents represent a simple
random sample of all potential respondents within the
community, and that the population is
large enough that application of the finite population correction
would not make an appreciable
difference in the results.
Managers associated with shopping areas like these find it
useful to have point estimates
regarding variables describing the characteristics and behaviors
of their customers. In addition, it
is helpful for them to have some idea as to the likely accuracy
of these estimates. Therein lies the
benefit of the techniques presented in this module and applied
here.

14. 1. Item C in the description of the data collection instrument
lists variables 7, 8, and 9, which
represent the respondent’s general attitude toward each of the
three shopping areas. Each of
these variables has numerically equal distances between the
possible responses, and for
purposes of analysis they may be considered to be of the
interval scale of measurement.
1. Determine the point estimate, and then construct the 95%
confidence interval for μ7 =
the average attitude toward Springdale Mall.
2. Repeat part (a) for μ8 and μ9, the average attitudes toward
Downtown and West Mall,
respectively.
2. Given the breakdown of responses for variable 26 (sex of
respondent), determine the point
estimate and then construct the 95% confidence interval for p26
= the population proportion of
males.
3. Given the breakdown of responses for variable 28 (marital
status of respondent), determine the
point estimate and then construct the 95% confidence interval
for p28 = the population
proportion in the “single or other” category.
4. Assume the managers have requested estimates of the mean
attitudes towards each mall with a
margin of error of 0.05 for each. If the managers want to have
95% confidence that the sample
mean will fall within this margin of error, how large should the
sample size be for each mall?

15. 1.The point estimate and the 95% confidence interval for μ7 =
the average attitude toward Springdale
Mall is
The point estimate
x
x
n
standard deviation
2
1
x x
SD
n

16. The 95% confidence interval for mean average attitude is
0.05/ 2, 1n
SD
x t
n
Count 150
Average 3.813
Standard
deviation 1.064
Standard error 0.087
t-significant value
at 5% 1.976
Point estimate 3.813
95% Lower limit 3.642
95% upper limit 3.985
2. The point estimate and the 95% confidence interval for μ8 =
the average attitude toward Down town

17. Mall is
The point estimate
x
x
n
standard deviation
2
1
x x
SD
n
The 95% confidence interval for mean average attitude is 0.05/
2, 1n
SD

18. x t
n
Count 150
Average 3.407
Standard deviation 1.124
Standard error 0.092
t-significant value at 5% 1.976
Point estimate 3.407
95% Lower limit 3.225
95% upperlimit 3.588
3. The point estimate and the 95% confidence interval for μ9 =
the average attitude toward West Mall is
The point estimate
x

19. x
n
standard deviation
2
1
x x
SD
n
The 95% confidence interval for mean average attitude is 0.05/
2, 1n
SD
x t
n

20. Count 150
Average 3.287
Standard
deviation 1.183
Standard error 0.097
t-significant value
at 5% 1.976
Point estimate 3.287
95% Lower limit 3.096
95% upper limit 3.478
II The point estimate and the 95% confidence interval for p26 =
the population proportion of males is
Point estimate
No.of Males
p
n

21. 95% confidence interval for population proportion of males is
0.05/2
1p p
p Z
n
Count 150
No.of Males 64
No.of Females 86
Proportion of
Males 0.427
Z value at
0.05/2 level 1.960
Standard
error 0.040
Point
estimate 0.427

22. 95%
confidence
interval lower
limit 0.348
95%
confidence
interval upper
limit 0.506
III
The point estimate and the 95% confidence interval for p28 =
the population proportion in the “single or
other” category is
Point estimate
No.of single or other
p
n
95% confidence interval for population proportion single or
other is
0.05/2
1p p
p Z
n

23. Count 150
NO. of Single
or other 83
No.of
Married 67
Proportion of
single or
other 0.553
Z value at
0.05/2 level 1.960
Standard
error 0.041
Point
estimate 0.553
95%
confidence
interval
lower limit 0.474
95%
confidence
interval

24. upper limit 0.633
IV.
The estimated sample sizes for each of the sample with the
margin of error 0.05 with 95% confidence is
2
0.05/ 2
*
Sample size
Z SD
ME
SPRINGDALE DOWN TOWN WEST
Margin of error 0.05 0.05 0.05
Standard
deviation 1.064 1.124 1.183
Z-value at 0.05/2
level 1.96 1.96 1.96
Sample size 1741 1941 2152