STAT 1350 Lecture Notes - Lecture 18: Confidence Interval, American Vandal, Netflix
27 Apr 2018
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3/20/2018
Chapter 21: Confidence Intervals
â—Ź Statistics in the News
○ Headline: “Netflix Survey: Binge-Watching is Not Weird or Unusual”
â– A survey of a random sample of 3078 online tv watchers finds that 1876
watch 2-3 episodes in one sitting at least every week weeks
â– If we want to use this information to estimate the population proportion,
we would need to construct a confidence interval
â– N = 3078, ^p = 1876/3078
● Netflix and “Binge-Watching”
â—‹ A survey of a random sample of 3078 online tv watchers finds that 1876 watch 2-
3 episodes in one sitting at least every week weeks
â—‹ Use the above information to construct a 95% confidence interval ^p = 0.61, n =
3078
â–
â—‹ 0.61 +/- (1.960) times the square root of {(.61)(1-.61)}/3078 = 0.61 +/- .018 =
(.592, .628)
â—‹ Interpretation: I am 95% confidence that the population proportion is between
.592 and .628
● More on Netflix and “Binge-Watching
â—‹ We constructed a 95% confidence interval and that interval ended up being from
.592 to .628
â—‹ How would the interval change if we decided we wanted to be 99%
confidence? WIDER → Go back to table above ^
● One more thing about Netflix…
○ According to a 2017 survey of 60,000 Netflix viewers, the most “binge-watched”
show was American Vandal
â—‹ Question: We would expect a 95% confience interval based on a sample of size n
= 60,000 to be what?
â– A. Very wide
â– B. Very narrow
â– C. Not affected since sample size does not impact the width of a
confidence interval
â—Ź Go back to formal above ^
â—Ź Is a higher confidence level better?
â—‹ Not necessarily
â—‹ Accuracy vs. precision (confidence level relates to accuracy, width of interval
relates to precision)
â—‹ Think of what we are doing as a balancing act. We want to be as confidence as we
can be, but we also want to reduce the margin of error
â—‹ Increasing the sample size reduces the margin of error; increasing the
confidence level increases the margin of error. An interval that is too wide is
not very precise
â—Ź Top at Question
○ A 95% confidence interval is 34% ± 6%. A 90% confidence interval based on this
same sample would have:
â– A. The same center and a larger margin of error.
â– B. The same center and a smaller margin of error.
â– C. A larger margin of error and probably a different center.
â– D. A smaller margin of error and probably a different center.
â– E. The same center, but the margin of error changes randomly.
â—Ź Daylight Saving Time
â—‹ Headline: Myths and truths about Daylight Savings Time
â– According to a 2014 Rasmussen Poll of 1000 adult Americans, 47% of
these adults do not think it’s worth it to change our clocks
â– Use this information to construct a 90% confidence interval for the
population proportion
