Transcript THE LIFE OF

OVER BOOKED?
A FACEBOOK EXPERIMENT
To test the claim that
the average teenager
uses Facebook for only
5 hours a week
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• Own Facebook
account used
• Number
Assignment +
Random Digit
Table = SRS
•100 subjects
• Standardized
out of 594
Question
friends
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Facebook Empirical Data
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•Empirical data is translated into
appropriate graphical displays.
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Weekly Facebook
Time Boxplot
Weekly Facebook Time Histogram
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30
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q1
25
Hours
40
min
20
20
median
max
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q3
Frequency
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20
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0
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Hours
5
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Facebook.com claims that the average teenager spends five
hours a week using Facebook. [Using Facebook means actually
using its features and not just having it open]. I believe that a
teenager uses Facebook for longer than five hours a week.
𝐻𝑜 : μ = 5 hours
A teenager uses Facebook an average of 5 hours a week
𝐻𝑎 : μ > 5 hours
A teenager uses Facebook for longer than 5 hours a week
n = 100
∝ = 5%
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A One Sample Mean T-Test…because the population
standard deviation is unknown & a mean ≠
proportion
Conditions:
•The distribution is an SRS
•Due to the Central Limit Theorem
(CLT) the population is normal since
n>40
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𝑥−𝜇
𝑡= 𝑠
𝑛
𝑡=
20.23−5
8.32
100
t = 18.3
Using TI-83 T-test: p-value = .00000000007
* Can not sketch critical region/value because p-value is too small
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A mean of 20 hours would occur .000007% of the time if the
population mean is 5 hours. So we can safely reject 𝐻 at
𝑜
the 5% significance level. And conclude that a teenager
uses Facebook for more than 5 hours a week!
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I want to estimate the mean time a teenager spends
on Facebook a week.
Since we do not know 𝜎 , I will use the one sample t-interval.
The data was collected via a random experiment. Due to
the Central Limit Theorem (CLT) the population is normal
since n>40
Confidence Interval = 95%
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𝑥±𝑡
∗
𝑠
𝑛
20 ± (1.984)
8.32
100
= 18.579 to 21.881 hours
I am 95% confident that the mean time a teenager spends on
Facebook a week is between 18.579 to 21.881 hours
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Strengths & Weaknesses…
Standardized
Question
Only My FB
Friends
Inaccurate
Answers
Population Mean
is National
Unclear What
Type of Usage
Large # of
Subjects
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