Introduction
The making of purchasing choices forms a key aspect of ordinary life, with community members making decisions and preferences in places for making purchases. For the Springdale community, three key malls exists, which makes a significant impact on their decisions. This study examines survey data, with the evaluation of various interest variables relating to shopping malls in Springdale. Through the analysis, there is the making of summative conclusions, on the most and less preferred shopping mall, essential in acting as a prerequisite for explaining community member’s behaviors.
Data Analysis and Discussion
Point estimate and 95% confidence interval for µ7 = average attitude toward Springdale Mall
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Point estimate
𝑥 ̅ 7 = 3.65, 𝑠 7 = 1.25
95% confidence interval
𝑥 ̅ ± Z 𝑎 ⁄2 ∙ 𝑠 √ 𝑛
𝑎 /2 = (1 − .95)/2= .025
( n ) = 150, ( n -1) = df = 149
Z 0.025 = 1.96
𝐿𝐵 (lower boundary) = 3.65 − (1.96∙ 1.25)/ √150 = 3.45
𝑈𝐵 (upper boundary) = 3.65 + (1.96∙ 1.25)/ √150 = 3.85
Our 95% confidence interval is (3.45, 3.85)
We are 95% confident that the mean attitude toward Springdale Mall is between 3.45 and 3.85.
| SPRILIKE | |
| Mean | 3.646666667 |
| Standard Deviation | 1.253915568 |
| n | 150 |
| (n-1) | 149 |
| confidence level | 0.200037987 |
| lower boundary | 3.44662868 |
| upper boundary | 3.846704653 |
Point estimate and 95% confidence interval for µ8 = average attitude toward Downtown Mall
Point estimate
𝑥 ̅ 8 = 3.43, 𝑠 8 = 1.15
95% confidence interval
𝑥 ̅ ± Z 𝑎 ⁄2 ∙ 𝑠 √ 𝑛
𝑎 /2 = (1 − .95)/2= .025
( n ) = 150, ( n -1) = df = 149
Z 0.025 = 1.96
𝐿𝐵 (lower boundary) = 3.43 − (1.96∙ 1.15)/ √150 = 3.25
𝑈𝐵 (upper boundary) = 3.43 + (1.96∙ 1.15)/ √150 = 3.61
Our 95% confidence interval is (3.25, 3.61)
We are 95% confident that the mean attitude toward Springdale Mall is between 3.25 and 3.61.
| DOWNLIKE | |
| Mean | 3.426666667 |
| Standard Deviation | 1.148951472 |
| n | 150 |
| (n-1) | 149 |
| confidence level | 0.184034948 |
| lower boundary | 3.242631719 |
| upper boundary | 3.610701614 |
Point estimate and 95% confidence interval for µ9 = average attitude toward West Mall
Point estimate
𝑥 ̅ 9 = 3.16, 𝑠 9 = 1.16
95% confidence interval
𝑥 ̅ ± Z 𝑎 ⁄2 ∙ 𝑠 √ 𝑛
𝑎 /2 = (1 − .95)/2= .025
( n ) = 150, ( n -1) = df = 149
Z 0.025 = 1.96
𝐿𝐵 (lower boundary) = 3.16 − (1.96∙ 1.16)/ √150 = 2.97
𝑈𝐵 (upper boundary) = 3.16 + (1.96∙ 1.16)/ √150 = 3.35
Our 95% confidence interval is (2.97, 3.35)
We are 95% confident that the mean attitude toward West Mall is between 2.97 and 3.35.
| WESTLIKE | |
| Mean | 3.16 |
| Standard Deviation | 1.164808363 |
| n | 150 |
| (n-1) | 149 |
| confidence level | 0.185635251 |
| lower boundary | 2.974364749 |
| upper boundary | 3.345635251 |
Point estimate and 95% confidence interval for p26 = the population proportion of males
Point estimate
𝑝 ̂ 26 = 𝑥 /n
𝑥 (males) =64
Sample size (n) = 150
𝑝 ̂ 26 = 64 /150 = 0.43
95% confidence interval
𝑝 ̂ ± Z 𝑎 ⁄2 ∙ √ 𝑝 ̂ (1− 𝑝 ̂)/ 𝑛
𝑎 /2 = (1 − .95)/2= .025
( n ) = 150, ( n -1) = df = 149
Z 0.025 = 1.96
𝐿𝐵 (lower boundary) = 0.43 − 1.96∙ √0.43 (1-0.43)/150 = 0.35
𝑈𝐵 (upper boundary) = 0.43 + 1.96∙ √0.43 (1-0.43)/150 = 0.51
95% confidence interval for the proportion of males is (0.35, 0.51)
We are 95% confident that the population proportion of males is between 0.35 and 0.51
| Row Labels | Count of RESPGEND |
| 1 | 64 |
| 2 | 86 |
| Grand Total | 150 |
| Proportion(males) | |
| n | 150 |
| x(number of males) | 64 |
| 𝑝 ̂ | 0.426667 |
| Margin of error | 0.079151 |
| lower boundary | 0.347515 |
| upper boundary | 0.505818 |
Point estimate and 95% confidence interval for p28 = the population proportion in the “single or other” category
Point estimate
𝑝 ̂ 28 = 𝑥 /n
𝑥 (single or other) =84
Sample size (n) = 150
𝑝 ̂ 26 = 84 /150 = 0.56
95% confidence interval
𝑝 ̂ ± Z 𝑎 ⁄2 ∙ √ 𝑝 ̂ (1− 𝑝 ̂)/ 𝑛
𝑎 /2 = (1 − .95)/2= .025
( n ) = 150, ( n -1) = df = 149
Z 0.025 = 1.96
𝐿𝐵 (lower boundary) = 0.56 − 1.96∙ √0.56 (1-0.56)/150 = 0.48
𝑈𝐵 (upper boundary) = 0.56 + 1.96∙ √0.56 (1-0.56)/150 = 0.64
95% confidence interval for the proportion of males is (0.48, 0.64)
We are 95% confident that the population proportion of single or other category of respondents is between 0.48 and 0.64
| Row Labels | Count of RESPMARI |
| 1 | 66 |
| 2 | 84 |
| Grand Total | 150 |
| Proportion(single or other) | |
| n | 150 |
| x(single or other) | 84 |
| 𝑝 ̂ | 0.56 |
| Margin of error | 0.079438 |
| lower boundary | 0.480562 |
| upper boundary | 0.639438 |
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?
Springdale Mall
𝑛 = (Z 𝑎 ⁄2 ∙ 𝑠 / 𝐸 ) 2
𝐸 (margin of error) = 0.05
Z 𝑎 ⁄2 = 1.96
𝑠 7 = 1.25
𝑛 7 = (1.96∙1.25/0.05) 2
𝑛 7 = 2,401
Springdale Mall would need 2,401 respondents for the survey
Downtown Mall
𝑛 = (Z 𝑎 ⁄2 ∙ 𝑠 / 𝐸 ) 2
𝐸 (margin of error) = 0.05
Z 𝑎 ⁄2 = 1.96
𝑠 8 = 1.15
𝑛 8 = (1.96∙1.15/0.05) 2
𝑛 8 = 2,032
Downtown Mall would need 2,032 respondents for the survey
West Mall
𝑛 = (Z 𝑎 ⁄2 ∙ 𝑠 / 𝐸 ) 2
𝐸 (margin of error) = 0.05
Z 𝑎 ⁄2 = 1.96
𝑠 9 = 1.16
𝑛 9 = (1.96∙1.16/0.05) 2
𝑛 9 = 909
West Mall would need 909 respondents for the survey
Conclusion
We can conclude that Springdale mall is the most suitable shopping area for local residents. Respondents have a moderate liking towards Downtown mall; their average attitude is between “like” and “neutral". Westmall is least preferred; participants’ average attitude towards West mall was neutral. Proportion of males was found to be less than half; we can make the conclusion that there are more female participants in the survey than males. Married individuals were less compared to those in the single or other category.
