# Springdale

### Option #1: Springdale Shopping Survey

Instructions

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

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CODING

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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.

• 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.
• Determine the point estimate, and then construct the 95% confidence interval for ?7= the average attitude toward Springdale Mall.
• Repeat part (a) for ?8 and ?9, the average attitudes toward Downtown and West Mall, respectively.
• Given the breakdown of responses for variable 26 (sex of respondent), determine the point estimate, and construct the 95% confidence interval for p26= the population proportion of males.
• 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.
• Assume the managers have requested estimates of the mean attitudes towards each mall with a margin of error of 0.05 for each mall. 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?
• Springdale Shopping Survey*
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 were as follows:
A. How Often Respondent Shops at Each Area (Variables 1–3)
1.
Springdale Mall
2.
Downtown
3.
West Mall
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
6 or more times/wk.
4–5 times/wk.
2–3 times/wk.
1 time/wk.
2–4 times/mo.
0–1 times/mo.
B. How Much the Respondent Spends during a Trip to Each Area (Variables 4–6)
4.
Springdale Mall
5.
Downtown
6.
West Mall
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
7.
Springdale Mall
8.
Downtown
9.
West Mall
(5)
(4)
(3)
(2)
(1)
(5)
(4)
(3)
(2)
(1)
(5)
(4)
(3)
(2)
(1)
\$200 or more
\$150–under \$200
\$100–under \$150
\$ 50–under \$100
\$ 25–under \$50
\$ 15–under \$25
less than \$15
C. General Attitude toward Each Shopping Area (Variables 7–9)
Like very much
Like
Neutral
Dislike
Dislike very much
D. Which Shopping Area Best Fits Each Description (Variables 10–17)
10. Easy to return/exchange goods
11. High quality of goods
12. Low prices
13. Good variety of sizes/styles
15. Convenient shopping hours
16. Clean stores and surroundings
17. A lot of bargain sales
Springdale
Mall
Downtown
West
Mall
No
Opinion
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
E. Importance of Each Item in Respondent’s Choice of a Shopping Area (Variables 18–25)
Not
Important
18. Easy to return/exchange goods
19. High quality of goods
20. Low prices
21. Good variety of sizes/styles
23. Convenient shopping hours
24. Clean stores and surroundings
25. A lot of bargain sales
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
Very
Important
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(6)
(6)
(6)
(6)
(6)
(6)
(6)
(6)
(7)
(7)
(7)
(7)
(7)
(7)
(7)
(7)
F. Information aboutt the Respondent (Variables 26–30)
26. Gender: (1) = Male
(2) = Female
27. Number of years of school completed:
(1) = less than 8 years
(3) = 12–under 16 years
(2) = 8–under 12 years
(4) = 16 years or more
28. Marital status: (1) = Married (2) = Single or other
29. Number of people in household:
persons
30. Age:
years
Each respondent in this database is described by 30 variables. As an example of their interpretation, consider row number 1.
This corresponds to respondent number 1 and contains the following information.
Variable number 6 = 7. The
respondent usually spends less
than \$15 when she
shops at West Mall.
Variable number 26 = 2. The
respondent is a female.
5556774441131111167765667232421
Variable number 1 = 5.
The respondent shops at Springdale Mall 2–4 times/month.
Variable number 19 = 7.
Respondent believes “high quality
of goods” is very important in
choosing a shopping area.
*Source: Materials for this case have been provided courtesy of The Archimedes Group, Indiana, PA. Data are based on actual responses
obtained to this subset of the questions included in the survey; town and mall identities have been disguised as well as a number of
responses were updated.
1
Running head: OPTION #1 SPRINGDALE SHOPPING SURVEY
Option #1 Springdale Shopping Survey
Tiffany Ferguson
MTH156: Introduction to Statistics
Dr. Kirsten Messer
November 15, 2019
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2
OPTION #1 SPRINGDALE SHOPPING SURVEY
Option #1 Springdale Shopping Survey
There were three malls in the area: Springdale Mall, Downtown Mall, and West Mall. A
survey was conducted by telephone. One hundred fifty people answered a series of 30 questions.
The focus of this discussion will be the variables 7,8, & 9 which represent the respondent’s
general attitude toward each of the three shopping areas, variable 26 which represents the gender
of the respondents, and variable 28 which represent the marital status of respondents (Anderson,
Sweeney, & Williams, 2016).
Variables 7-9 are rated as follows:

Like very much (5)

Like (4)

Neutral (3)

Dislike (2)

Dislike very much (1)
Variables 26 is : (1) Male and (2) Female
Variables 28 is : (1) Married and (2) Single or Other
Each of the variables has numerically equal distance between the possible response, and for
analysis, they may be considered to be an interval scale of measurement.
Point of estimate and 95% confidence interval for µ7 = average attitude toward Springdale
Mall
The point estimate is the mean 3.707 (rounded three decimal places). This indicates that
Springdale Mall is rated between Like and neutral, which is neither liked very much or dislike
very much. The confidence interval is (3.507, 3.906) rounded three decimal places. Therefore, it
means there is 95% confidence that the true population mean is between 3.50748454 and
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3
OPTION #1 SPRINGDALE SHOPPING SURVEY
3.9058488. The maximum likely error in the estimate of the population is found to be 0.199
(rounded three decimal places).
Point of estimate and 95% confidence interval for µ8 = average attitude toward Downtown
Mall
The point estimate is the mean of 3.38. This indicates that Downtown Mall is rated
between Like and neutral, which is neither liked very much or dislike very much. The confidence
interval is (3.205, 3.555) rounded three decimal places. Therefore, it means there is 95%
confidence that the true population mean is between 3.204732496 and 3.555267504. The
maximum likely error in the estimate of the population is found to be 0.175 (rounded three
decimal).
Point of estimate and 95% confidence interval for µ9 = average attitude toward West Mall
The point estimate is the mean 3.167 (rounded three decimal places), this indicates that
West Mall is rated between Like and neutral, which is neither liked very much or dislike very
much. The confidence interval is (2.965, 3.368) rounded three decimal places. Therefore, it
means there is 95% confidence that the true population mean is between 2.96497966 and
3.368353674. The maximum likely error in the estimate of the population is found to be 0.202
(rounded three decimal places).
Point of estimate and 95% confidence interval for p26 = population proportion of males
Second, variable 26 is (1) for males and (2) for females. The sample size 150, and the
number of males is 62. Therefore, the sample proportion (point of estimate) is 0.413 (rounded
three decimal places), and constructing a confidence interval of 95% for the population
proportion of males is (0.374, 0.453) rounded three decimal places. Thus, there is 95% confident
that the true proportion of males are between 0.3739306 and 0.45273607
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4
OPTION #1 SPRINGDALE SHOPPING SURVEY
Point of estimate and 95% confidence interval for p28 = population proportion of “single or
other.”
Lastly, the variable 28 is (1) for married and (2) for “single or other.” The sample size
150 and the number of “single or other” is 76. Therefore, the sample proportion (point of
estimate) is 0.507 (rounded three decimal places), and constructing a confidence interval of 95%
for the population proportion of “single or other” is (0.467, 0.547) rounded three decimal places.
Thus, there is 95% confident that the true proportion of “single or other” is between 0.46666189
and 0.54667144
Sample Sizes
It is assumed that the managers have requested estimates of the mean attitudes towards each
mall, with a margin of error of 0.05. Given that there is a 95% confidence that the sample means
will fall within this margin of error, the sample sizes would be as follows:

Springdale Mall – 2,342

Downtown Mall – 1,829

West Mall – 2,422
Conclusion
In conclusion, if comparing the general attitude of each of the three shopping centers, it is
indicated that Springdale is liked more than Downtown and West. West Mall’s general attitude is
liked the least. These numbers can help understand behaviors so that the store owners can
improve their companies. For instance, if it was agreed to shut down one of the malls and they
went solely on these population proportion calculations, then West Mall would be the mall to go.
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5
OPTION #1 SPRINGDALE SHOPPING SURVEY
It is also learned that there are more female shoppers than males. However, with the confidence
interval of 95% for p28 = population proportion of “single or other” being (0.467, 0.547), it is
possible for married and “single or other” be an equal proportion.
Furthermore, to obtain information about the desired outcomes, the sample size needs to
be considered. For example, using 0.05 as the margin of error given that the confidence level of
95%, the managers in Springdale mall would have to survey 2,342 people to be a more
reasonable distribution and get to the true mean. The point of estimate and confidence interval
are ways for businesses to get a more realistic overall picture of want the customer wants.
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6
OPTION #1 SPRINGDALE SHOPPING SURVEY
References
Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2016). Essentials of modern business
statistics: with Microsoft Office Excel (6th ed.). Boston, MA: Cengage Learning.
Colorado State University-Global Campus. (2019). MTH156-2: Module 6: Sampling
https://portal.csuglobal.edu/portal/student
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1
Data Option #1: Springdale Shopping Survey
Angelia Stansbury
MTH156: Introduction to Statistics
Dr. Michael Urban
June 20, 2021
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2
Springdale Shopping Survey
In order to make a determination of the area malls individuals may favor, a survey on the
telephone was completed. One hundred Fifty individuals were surveyed and were requested to
rate each mall in regards to its strengths and weaknesses utilizing a Likert scale. This report will
be examining the confidence intervals for the general attitude of each shopping area and the
population proportions for gender and marital status of the respondents in a hope to acquire
accurate point estimates of these variables.
General Attitude Results
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The point estimate of the mean attitude toward Springdale Mall is seen as 3.8323. The
maximum likely error in the point estimate of the population mean attitude toward Springdale
Mall is 0.2477. The answer is found by calculating the difference of the Interval Upper Limit and
the Interval Lower Limit then dividing the sum by two (4.3277-3.8323/2 = 0.2477). The
information is also provided above on the chart listed as the Interval Half width.
Downtown and West Mall
The point estimate of the mean attitude toward the Downtown shopping area is seen as
4.2133. The maximum likely error in the point estimate of the population mean attitude toward
the Downtown shopping area is 0.2414. The answer is found by calculating the difference of the
Interval Upper Limit and the Interval Lower Limit then dividing the sum by two (4.4548-
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4
3.9719/2 = 0.2414). The information is also provided above on the chart listed as the Interval
Half width.
The point estimate of the mean attitude toward the West Mall is seen as 4.3267. The
maximum likely error in the point estimate of the population mean attitude toward the West Mall
is 0.2414. The answer is found by calculating the difference of the Interval Upper Limit and the
Interval Lower Limit then dividing the sum by two (4.5680-4.0853/2 = 0.2414). The information
is also provided above on the chart listed as the Interval Half width.
Gender
The below charts provides information on the breakdown of responses for variable 26
(gender of respondents) in regards to the point estimate and the 95% confidence interval for
p26= the population proportion of males.
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5
The point estimate of the population proportion that is male is 0.4067. The maximum
likely error in the point estimate of the population proportion of males is 0.0794. The answer is
found by calculating the difference of the Interval Upper Limit and the Interval Lower Limit then
dividing the sum by two (1.6527-1.4939/2 = 0.0794). The information is also provided above on
the chart listed as the Interval Half width.
Marital Status
The below charts provides information on the breakdown of responses for variable 28
(marital status of respondent) in regards to the point estimate and the 95% confidence interval for
p28 = the population proportion in the “single or other” category.
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6
The point estimate of the population proportion that is “single or other” is 0.5533. The
maximum likely error in the point estimate of the population proportion of males is 0.0798. The
answer is found by calculating the difference of the Interval Upper Limit and the Interval Lower
Limit then dividing the sum by two (1.6332 – 1.4735 / 2 = 0.0798). The information is also
provided above on the chart listed as the Interval Half width.
The estimated sample size for the managers who wish to know estimates of the mean
attitudes in reference to each mall and the margin of error should be referred to utilize the
provided sample sizes listed as follows:
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7
Conclusion
To conclude, shoppers frequently enjoy shopping at the Springdale Mall, meanwhile the
perspective in regards to the Downtown Mall and West Mall are more neutral. In addition, one
may also determine the managers are able to be 95% certain the population proportion of males
is less than that of females. Finally, the population proportion of shoppers in the “single or other
category” is somewhat different from that of the shoppers which are married.
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8
Reference
Anderson, D., Sweeney, D., & Williams, T. (2015). Modern Business Statistics With Microsoft
Office Excel (5th ed.). Stamford, CT: Cenage Learning.
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