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Vanilla Bear & Chocolate Bear's Excellent Statistics Presentation
Transcript of Vanilla Bear & Chocolate Bear's Excellent Statistics Presentation
Period 6 The Average User. . . Let's compare the average number of friends the Facebook user from Lynbrook has with the average number of friends the population of Facebook users has and see if Lynbrook students have
the larger mean. We are testing the null hypothesis that
both averages are equal against the alternate hypothesis that Lynbrook students' average number of friends is greater than the global average.
Ho: μ(LHS) = μ(Globe)
Ha: μ(LHS) > μ(Globe) freshmen sophomores juniors seniors females males 582 460 543 409 784 600 521 544 The Average Lynbrook . . . BOY GIRL has 497
friends. has 587
friends. The Average has 541 friends. μ μ μ Ho: μ(LHS) = μ(Globe)
Ha: μ(LHS) > μ(Globe) t-score: _______ 242.3/√115 541 - 130 = 18.2 p(T > 18.2) = 0 At an alpha level of 0.05, we the null
hypothesis. REJECT The observed results are not likely due to chance. On average, Lynbrook students have a significantly greater average number of Facebook friends when compared to the global average. α The Moment
of Truth. . . Now, let's see if the proportions
of Lynbrook students who are listed as single or as being in a relationship are different from the matching proportions of all Facebook users. First, we'll calculate the proportions
of the various relationship statuses
of Lynbrook students. Observations 78% of Lynbrook students are listed as single 75% of Lynbrook females
say they're single 81% of Lynbrook males
say they're single 19% 25% of Lynbrook females
say they're in a relationship of Lynbrook males
say they're dating of Lynbrook students are listed as being
married or in a relationship 22% 43% of the girls who say they are in a relationship list one of their close female friends as their significant other.
This figure constitutes 66% of freshmen girls and 50% of sophomore girls, which suggests that this is somewhat of a trend among underclassmen females. HOWEVER, Pictured above: A failed attempt to start a new relationship trend on Facebook.
They know us too well. Ho: p(single LHS students) = p(Globe)
Ha: p(single LHS students) ≠ p(Globe)
p(single LHS students) = 0.78
p(single Facebook users) = 0.31 Let's look at the single students, because no one is interested in people who are already in relationships. Unless they're married to their best friend. Then go for it. We run a one proportion z-test to calculate a z-score of 10.9 and a p-value that is essentially zero.
At any reasonable α-level, we have very strong evidence to reject the null hypothesis. In conclusion, on average, the proportion of Lynbrook students who are listed as single is significantly different from the proportion of all Facebook users that say they are single. Pictured above: A volatile relationship. LYNBROOK GIRL LYNBROOK BOY Let's break down relationship
status by gender now. Ho: p(single males at LHS) = p(single Facebook males)
Ha: p(single males at LHS) ≠ p(single Facebook males)
We run a one proportion z-test and calculate the z-score
to be 7.7 and the p-value to be approximately zero. Ho: p(SINGLE Lynbrook LADIES) = p(single Facebook girls)
Ha: p(SINGLE Lynbrook LADIES) ≠ p(single Facebook girls)
α-level = 0.05
We run a one proportion z-test and calculate the z-score
to be 9.3 and the p-value to be approximately zero. Both tests achieved statistical significance at (and beyond) the p = 0.01
level. From this, we can conclude that the results are not likely due to chance and that, on average, the proportions of single male and female Facebook users at Lynbrook is significantly different from the proportions of all single Facebook users.
Again, although we only performed two-sided tests, we can easily find
the values of the one-sided test testing if Lynbrook's proportions of
single students were greater than the population proportion. Null Hypothesis, We You! We find the one-sided test p-value by halving the two-sided test value. . . essentially zero / 2 = pretty much zero again Therefore, on average, the proportions of single male and female students at Lynbrook are significantly greater than the proportion of all single males and females on Facebook. But what can we really take away from this? » We cannot generalize these results to the population of Facebook users.
» A Lynbrook student has only two viable relationship statuses, “single” and “in a relationship,” while adults, who are not present in the sample, have the options of being “engaged,” “married,” “divorced,” “in a domestic partnership,” and so on.
» Lynbrook students are generally more interested in studying than in forming relationships online. SOURCES & we can't forget our lovely TI-83! Number of students in sample
(n) = 115
Standard deviation of number of friends
(s) = 242.3 (x-bar) » The age range of our sample was not representative of the age range of all Facebook users.
» Lynbrook students likely joined Facebook in the late 2000s when Facebook went public to all, and began adding friends early.
» High schoolers use Facebook for more frivolous means when compared to older users.
» Our sample comes from a very specific region of the United States. Interquartile range = Q3 - Q1
= 699 - 380
= 319 IQR x 1.5 = 478.5
Q1 - 478.5 = -98.5
Q3 + 478.5 = 1177.5 Pictured left: A typical Lynbrook student,
hard at work in the library.
Pictured right: The typical Lynbrook pastime, as illustrated by the average student. SUSPECTED
OUTLIERS Two freshmen females with 1407
and 1459 friends, respectively. Two junior students, one male with
1227 friends and one female with
1294 friends. But how much is "significantly greater"? Let's construct a confidence interval and find out! We calculate the 95% T-interval to be 541 friends plus or minus 45.
In other words, if this procedure was repeated many times, the 95% confidence interval would capture the true mean number of friends the Lynbrook student has on Facebook to be between the values of 496 and 586 friends, 95% of the time.
However, these results cannot be generalized to the entire population of Facebook users because the sample consisted only of Lynbrook students and is not representative of all users. But how significant is it? We calculate the 95% two proportion z-interval
and find that the difference between the two proportions is
47% plus or minus 8%.
This means that, if we were to calculate the 95% confidence
interval numerous times, we would find that, 95% of the time,
the difference between the proportions of single Lynbrook
students and all single Facebook users is between the values
of 39% and 55%. Our Sampling Method For this study, we performed a stratified random sample.
First, we picked an SRS of roughly 50 students from each grade using last year's yearbook. We used a full list of names of freshman we acquired from a class officer, and performed an SRS of those names as well.
Second, we manually checked each name on Facebook and selected every student 1) that had a Facebook and 2) whose profile showed us the number of friends they had.
We then collected the necessary data, organized it by grade and gender, and performed
our data analysis.