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Phase three: Flagler College Students and Online Shopping
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PHASE THREE: Opinions on Shopping among Flagler Students, 2018

Introduction:

My project was based on surveys given to 2018-2019 Flagler students. The first phase of my project involved calculating summary statistics and describing and defining the overall sample, which consisted of 150 students. This helped me get to know my data well enough to split the overall sample into two separate samples, based on their opinion about the future of shopping: one group believed that in-person stores would be obsolete, while the other group believed that in-person stores would still be relevant. Splitting the data in this way resulted in two similarly sized samples. There were 77 students in the no group (believing that online shopping was not the future) and 73 in the yes group (believing that it was the future).

Result 1, Bar Graph: Future of Shopping: Is it online?

Result 1: Bar Graph: Future of Shopping: Is it online?   [Info]
Right click to copy

My first step will be to use a statistical test of majority to decide if the sample results indicate that within the Flagler student population, a majority of the students like shopping in-store for clothes and shoes more than online.  In order to make the decision, I will perform a one-sample hypothesis test and see if there is a statistically significant result. A hypothesis test will first be run to find statistical evidence of majority and then a confidence interval will be constructed to estimate a range for the percentage of flagler students who prefer shopping for clothes and shoes in-store. A confidence interval is important and necessary because, while a hypothesis test tells us if the value is above or below 50%, the interval allows us to make a good guess at what the value is.

My second step will be to determine whether or not there is a difference in population proportion of gender between the students who think online shopping is the future of shopping and those who do not. First, I will complete a hypothesis test to determine if a difference exists, and then I will create a hypothesis test to estimate the difference between the groups.


Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 114 claimed that they preferred shopping in store, compared to 36 students who answered that they preferred shopping for clothes and shoes online.  A majority, 76%, of the students in the sample preferred to shop in-store. These results will be used to test the claim that the majority of the population of Flagler College students prefer shopping for shoes and clothing in-store at 95% confidence (a level of significance of 0.05).  The data is represented in a pie chart below.

Result 2: Pie Chart With Data -Do Flagler students prefer shopping for clothes and shoes in store?

Result 2: Pie Chart With Data -Do Flagler students prefer shopping for clothes and shoes in store?   [Info]
Right click to copy

 

 

Hypothesize

         Null: Fifty percent of all Flagler College students prefer shopping for clothes and shoes in-store

         Alternate: More than 50% of all Flagler College students prefer shopping for clothes and shoes in-store

Having ‘more than’ in our alternative hypothesis lets us know that this is a upper-tailed (right-tailed) test

Prepare

         1. Random Sample –We assume that the sample is random enough to be representative

         2. Large Sample – n*p0 = (150) (0.50) = 75 > 10 and n*(1-p0) = (150) (0.50) = 75 > 10

Since both  n*p0 and n*(1-p0) are greater than 10, we have a large enough sample size for inference

         3. Big Population –The population of students at Flagler college is about 2,500. Our sample must be smaller than 10% of the total population size. Since 10n = (10)(150) = 1500 < 2500, the population is big enough for inference.  

         4. Independence within Sample – Yes, we can assume that whatever a particular student answered does not have any effect on the other responses in the sample.

Compute

Result 3: One sample proportion hypothesis test- in-store shopping

 

Result 3: One sample proportion hypothesis test   [Info]

One sample proportion hypothesis test:


Outcomes in : Sample(Shoes and Clothing - Online or Store)
Success : In store
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5

Hypothesis test results:
VariableCountTotalSample Prop.Std. Err.Z-StatP-value
Sample(Shoes and Clothing - Online or Store)1141500.760.0408248296.3686733<0.0001

Interpretation

When the p-value (less than 0.0001) is less than alpha (the level of significance of 0.05), the null hypothesis will be rejected.  It is possible to say that there is sufficient evidence to conclude that the true population proportion of Flagler students who prefer shopping in store for shoes and clothing is greater than 0.5.




Confidence Interval #1 – Estimating the Population Proportion

         The hypothesis test found evidence of a proportion greater than 0.5. The next step is to construct a confidence interval to give us an estimate of the true population proportion of Flagler students who prefer shopping for clothes and shoes in store. Because our hypothesis test was based on a right-tailed test with a significance level of 0.05, the confidence level for the interval should be 90%.

Prepare

         1. Random Sample with Independent Observations – We assume that the sample is random enough to be representative, and we assume that individual responses from participants did not affect the responses of other participants

         2. Large Sample – Since n*p-hat = (150)(0.76) = 114 > 10 and n*(1 – p-hat) = (150)(1 – 0.76) = (150)(0.24) = 36 > 10, the sample is big enough.

         3. Big Population – The population of students at Flagler college is about 2,500. Our sample must be smaller than 10% of the total population size. Since 10n = (10)(150) = 1500 < 2500, the population is big enough for inference.  

Compute

Result 4: One sample proportion summary confidence interval - Distraction   

 

Result 4: One sample proportion confidence interval   [Info]

One sample proportion confidence interval:


Outcomes in : Sample(Shoes and Clothing - Online or Store)
Success : In store
p : Proportion of successes
Method: Standard-Wald

90% confidence interval results:
VariableCountTotalSample Prop.Std. Err.L. LimitU. Limit
Sample(Shoes and Clothing - Online or Store)1141500.760.0348711920.702641990.81735801

Interpret

We are 90% confident that the true percentage of Flagler students who prefer shopping in-store for clothing and shoes is between 65.3% and 77.4%. This supports our findings from the hypothesis test, that the population proportion is greater than 0.5.

 

Hypothesis Test #2 – A Claim of the Difference between two Population Proportions

A 2 by 2 contingency table was created to compare the opinions of the two samples of students (those who believed the future of shopping was online, and those who did not) with respect to whether or not they prefer to shop in-store or online for clothing and shoes. Of the 73 students who thought that the future of shopping was online, 50 of them preferred shopping in store, and of the 77 students who did not think that the future of shopping was online, 64 of them preferred shopping in store. 68.5% (50 out of 73 students) of those students who thought the future of shopping was online preferred shopping in store, while 83.1% (64 out of 77 students) of those students who did not think the future of shopping was online preferred shopping in store. Since this is about a 15% difference between the groups, we want to investigate further to see if the true proportion of students who prefer doing their shopping in store differs between the two populations (those who believe the future of shopping is online, and those who do not).

Result 5: Contingency table- Future of Shopping versus Shopping Preference

 

Result 5: Contingency table- Future of Shopping versus Shopping Preference   [Info]

Contingency table results:


Rows: Sample(Future of Shopping)
Columns: Sample(Shoes and Clothing - Online or Store)
In storeOnlineTotal
No641377
Yes502373
Total11436150

Chi-Square test:


StatisticDFValueP-value
Chi-square14.39353360.0361

The next step will be to use a hypothesis test to decide if there is a statistically significant difference among these two populations of Flagler students (those who believe the future of shopping is online, and those who do not). An alpha (level of significance) of 0.05 will be used.

Hypothesize

Null: The proportion of students who prefer to shop in store is not different between the population of students who think that the future of shopping is online and the population of students who do not think the future of shopping is online (another way of stating the null is to say that the difference in proportion between the two populations is equal to zero).

Alternate: The proportion of students who prefer to shop in store is different between the population of students who think that the future of shopping is online and the population of students who do not think the future of shopping is online (another way of stating the null is to say that the difference in proportion between the two populations is not equal to zero).

Since our alternate hypothesis is not equal to, this is a 2-tailed test.

Prepare:

1.   Large Samples

p-hat = (x1 + x2)/(n1 + n2) = (64 + 50)/(77 + 73) = 114/150 = 0.76

Sample One (Social Students): n1*p-hat = (77)(0.76) = 58.5 > 10 and

n1*(1 - p-hat) = (77)(1 – 0.76) = (77)(0.24) = 18.5 > 10. Since all of these values are greater than or equal to ten, sample one is large enough.

Sample Two (Unsocial Students): Since n2*p-hat = (73)(0.76) = 55.5 > 10 and

n2*(1 - p-hat) = (73)(1 – 0.76) = (73)(0.24) = 17.5 > 10, Since all of these values are greater than or equal to ten, sample two is large enough.

2. Random Samples – Although we are not sure, we assume that they are representative and proceed as if they were random.

3. Independent Samples – Yes, since each participant’s answers should not affect or be influenced by the responses of any other student.

4. Independence between Samples – We assume that there is no association between the students who believe the future of shopping is online, and those who do not.

 

Compute

Result 6: Two sample proportion summary hypothesis test - Shopping Preferences between 2 populations with different views on the future of shopping

 

Result 6: Two sample proportion hypothesis test   [Info]

Two sample proportion hypothesis test:


p1 : Proportion of successes (Success = In store) for Sample(Shoes and Clothing - Online or Store) where "Sample(Future of Shopping)" = "No"
p2 : Proportion of successes (Success = In store) for Sample(Shoes and Clothing - Online or Store) where "Sample(Future of Shopping)" = "Yes"
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 ≠ 0

Hypothesis test results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.Z-StatP-value
p1 - p2647750730.146237320.0697671942.09607580.0361

Interpret

Since the p – value = 0.0361 is less than the level of significance of 0.05, we reject the null hypothesis, and say that we found sufficient evidence that there is a difference in proportion of shopping preference (in store) between the population of students who believe the future of shopping is online and the population of students who do not believe the future of shopping is online.

 

Confidence Interval #2 –Estimate the Difference between two Population Proportions

Since we rejected our null hypothesis, the hypothesis test lets us conclude that there is a significant difference in the proportion of students who prefer shopping in store for clothing and shoes between the population of students who think that the future of shopping is online and the population of students who do not think that the future of shopping is online. Our next step is to use a confidence interval to estimate what the value of the difference in proportion is. Unlike our last confidence interval, which was one-tailed, our alternative hypothesis this time is two-tailed, with an alpha/significance level of 0.05. Therefore we will make a 95% confidence interval.

Prepare

         1. Random Samples with Independent Observations – Again, probably not (but we hope it is representative).  However, to proceed, we will assume it is. Furthermore, yes, the student responses were taken in such a way that their responses were independent of each other.

2. Large Samples

Sample One (Those who do not think online is the future of shopping): n1*p-hat1 = (77)(0.831) = 64 > 10 and n1*(1 - p-hat1) = (77)(1 – 0.831) = (77)(0.169) = 13 > 10. Since all of these values are greater than or equal to ten, sample one is large enough.

Sample Two (Those who do think that online is the future of shopping):  2*p-hat2 = (73)(0.685) = 50 > 10 and n2*(1 - p-hat2) = (73)(1 – 0.685) = (73)(0.315) = 23 > 10. Since all of these values are greater than or equal to ten, sample two is large enough.

3. Big Populations – The population of students at Flagler college is about 2,500. To be conservative, we assume that around 50% of all students at Flagler believe the future of shopping is online, and 50% do not. There should be around 1250 students in each population ((0.50)*2500)= 1250). Each sample must be smaller than 10% of the total population size..  

Population One (Future of Shopping: Not Online): Since 10n1 = (10)(77) = 770 < 1250, population one is large enough.

Population Two (Future of Shopping: Online): Since 10n2 = (10)(73) = 730 < 1250, population two is large enough.

4. Independent Samples – Again, we can assume that individual responses did not affect other responses and that the groups were independent.

Compute

Result 7: Two sample proportion summary confidence interval - Shopping Preferences between 2 populations with different views on the future of shopping

Result 7: Two sample proportion confidence interval   [Info]

Two sample proportion confidence interval:


p1 : Proportion of successes (Success = In store) for Sample(Shoes and Clothing - Online or Store) where "Sample(Future of Shopping)" = "No"
p2 : Proportion of successes (Success = In store) for Sample(Shoes and Clothing - Online or Store) where "Sample(Future of Shopping)" = "Yes"
p1 - p2 : Difference in proportions

95% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p2647750730.146237320.069127420.010750070.28172458

Interpret

The confidence interval does not contain zero, and only contains positive numbers. This supports the conclusion that proportion of those who prefer in store shopping for clothing and shoes in the population of those who do not think the future of shopping is online is greater than the proportion in the population who do think the future of shopping is online. To interpret this interval, we can say that we are 95% confident that the true difference in proportion of shopping preference between the population of those who do not think the future of shopping is online and  population of those who do think the future of shopping is online is between 1.1% and 28.2%.

Conclusion

 

With the advent of companies like Amazon and the numerous delivery programs for everyday and essential items, a future without actual stores seems more and more possible every day. However, opinions still seem to show that shopping in a store is preferable to shopping online, especially for shoes and clothing. We found significant evidence to suggest that the majority of Flagler college students prefer shopping in store for shoes and clothing compared to shopping online for shoes and clothing. We estimated that between 65.3% and 77.4% of Flagler students prefer shopping in store, compared to online. We also found that those who did not think that future of shopping was online were much more likely to prefer shopping in store for clothing and shoes, with an estimated 1.1% to 28.2% of Flagler students. Although this was found to be a significant difference, the lower limit of the confidence interval is very close to zero, suggesting that the difference between the groups might not be very large at all. Still, it is logical that those students who prefer shopping in store might not be able to imagine a future where all shopping takes place online. It is also logical that those students who prefer shopping online can envision a future where that is the norm, and the convenience and low operating fees of online shopping have pushed out normal brick and mortar stores . Shopping for clothing and shoes is also very different from buying household items, groceries, electronics, or many other items. Although many other types of stores might soon be obsolete, my guess is that clothing stores will stick around for quite a while- at least until online dressing rooms exist!


Data set 1. Franco Donner- Flagler College Students and Online   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=88142">Phase three: Flagler College Students and Online Shopping</A>

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