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.

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

14. Sales staff helpful/friendly

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

22. Sales staff helpful/friendly

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

Colorado State University-Global Campus

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

distributions and statistical inference. [course content]. Retrieved from

https://portal.csuglobal.edu/portal/student

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1

Data Option #1: Springdale Shopping Survey

Angelia Stansbury

Colorado State University Global

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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