Marisa Hancock, Gabby Marquez-Garcia, Santiago Hernández
6 December 2018
Introduction:
In Phase Two of the project we addressed three different comparisons of two data sets, those who believe people will/will not do all of their shopping online, and the second group is those who believe shopping is/is not bad for local businesses. On this phase of the report, we’ll be looking at students who said that the future of shopping will be solely online, and those who did not.
Firstly, we will run a hypothesis test on the sample who believe that all shopping will be done online, to find if a majority believe this. Then, we’ll find a confidence interval to estimate what range the population percentage of those who believe future shopping will be done online.
Secondly, another hypothesis test will be run to determine if those who believe shopping will be done solely online and those who do not, find shopping online easier. Another confidence interval will be completed to find an estimate of what the population percentage could be.
Hypothesis Test #1:
In the sample of 150 students, 102 reported that shopping is easier to do online. That is, the majority, 68%, of the students sampled expressed that shopping is easier to do online. These sample results will be used to test the claim that the majority of the population of Flagler College students view shopping online as easier at a level of significance of 0.05 A pie chart of the data is given below.
Hypothesize
Null: Fifty percent of all Flagler College students believe that shopping online is easier.
Alternate: More than 50% of all Flagler College students believe that is easier to shop online.
Based on the alternate hypothesis, right-sided test as it is trying to prove that the majority (more than 50%) of the sample believed in shopping online as being easier, rather than simply looking for a change.
Prepare
1. Random Sample – We’ll assumed the sample is random.
2. Large Sample – 50% of the sample is 75, and we must have greater than 10 successes and 10 failures, so the sample is large.
3. Big Population – Ten times the sample is 1,500. The population is big. Flagler College has a population of 2,500 students.
4. Independence within Sample – Yes, the student responses were taken in such a way that their responses were independent of each other, resulting in one response per person.
Compute
Interpret:
The p-value resulted in more than 50% of all Flagler College students believe that shopping online is easier.
Confidence Interval #1:
The Hypothesis tests does not reject the claim that most Flagler students believe that shopping online is easier than shopping in-store. In order to determine the proportion of Flagler College students that believe that shopping online is easier, we will build a 90% confidence interval. We use a 90% confidence interval to determine an estimate of where the population proportion lies.
Prepare:
Assume that the sample is random and observations are independent.
Large Sample-Since n*phat = (150)(0.68) = 102 > 10 and n*(1 – phat) = (150)(1 – 0.68) = 48> 10, the sample is large.
Interpret:
We are 90% confident that the population proportion of Flagler College students who believe shopping online is easier, lies between 61.7% and 74.3%. This is over the majority, so it is obvious that the population proportion is not 50%.
Hypothesis Test #2:
Interpret:
We reject the null hypothesis. The p-value (0.0001) is smaller than the 0.05 significance level. There is sufficient evidence to determine that the two populations have different population proportions.
Hypothesis Test #2 – A Claim of the Difference between two Population Proportions:
The contingency table below compares population 1 (students who believe that we’ll do all of our shopping online in the future) and population 2 (students who don’t believe that we’ll do all of our shopping online in the future) with regard to the type of shopping they believe is easier. 57.32% (47/82) of population 1, and 80.09% (55/68) ofpopulation 2 thought that shopping online was easier. There is a difference of approximately 22.7% between the two samples, giving us a strong reason to believe that the two populations have different proportions.
The hypothesis test will determine whether there is a statistically significant difference (greater than the significance level of 0.05) for the two populations.
Hypothezise:
Null: there is no difference in proportion between the two populations. P1 = P2
Alternate: the two populations have different proportions P1 ≠ P2
1) Large samples- The pooled sample proportion is:
P̂= (x1 + x2)/(n1 + n2) = (55+ 47)/(68 + 82) = 102/150 = 0.68
Sample 1 (believethatall shopping in thefuturewill be done online): Since N1*P̂ = (68)*(0.68)=46.24>10 and N1*(1-P̂)̂= (68)*(0.32)=21.76>10.
Sample2 (don’tbelievethatallthe shopping in thefuturewill be done online): Since N2*P̂=(82)*(0.68)=55.76 and N2(1-P̂)=(82)*(0.32)=26.24>10.
2) Randomsamples- weassumethatthesamples are random.
3)Independent samples- the responses are independentfromeachother.
4)Independence betweensamples- thereis no relationshipbetweenthetwosamples.
Interpret
This confidence interval includes only negative values, which suggests that P2 is greater than P1; therefore, P1<P2 <0. In other words, the percentage of the population of those who do not believe that all the future shopping will be done online and who find shopping online easier, is less than the percentage of those believe all the shopping be done online and find shopping online easier. Hence, we are 95% confident that the percentage of students that disagree with all the future shopping being done online, and prefer not to shop online, is between 11.7% and 33.6% greater than the percentage of all students that believe in future of shopping done online who find shopping online easier.
Conclusion:
Consumerism is a topic that concerns many psychologists and society in general, as people have started to develop a desire to buy and buy, even when they don’t need to buy those items. Recently, with the development of the internet, people don’t even need to get out of their houses to purchase items with online shopping. In the last years, there has been a trend when more and more people rely on shopping online as it is less time-consuming and it gets delivered to their door. In this report, the sample provided evidence that the majority of all Flagler College students do their shopping online. In fact, it was estimated that between 61.7% and 74.3% of all Flagler College students identify as doing most of their shopping online. Furthermore, there is statistical evidence that show that those students who think that future of shopping will be done online and they tend to do more shopping online. It was estimated that between 11.7% and 33.6% more of all Flagler College students who believe that shopping will be done online tenf to find shopping online easier than all other Flagler College students. This is a logical statement, as people that tend to find buying online more convenient and easier, will believe that all the shopping will be done online in the future.
One of the main purposes of online shopping is to make more things accessible to people, and easy the time they spent in stores or when they don’t find something that they need. It is understandable how many students believe that all the future of shopping might be done online.
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One sample proportion summary hypothesis test:p : Proportion of successes H0 : p = 0.5 HA : p > 0.5 Hypothesis test results:
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One sample proportion summary confidence interval:p : Proportion of successes Method: Standard-Wald 90% confidence interval results:
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Two sample proportion summary hypothesis test:p1 : proportion of successes for population 1 p2 : proportion of successes for population 2 p1 - p2 : Difference in proportions H0 : p1 - p2 = 0 HA : p1 - p2 ≠ 0 Hypothesis test results:
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Contingency table results:
Rows: Future of Shopping) Columns: Online - Easier?)
Chi-Square test:
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Two sample proportion summary confidence interval:p1 : proportion of successes for population 1 p2 : proportion of successes for population 2 p1 - p2 : Difference in proportions 95% confidence interval results:
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