STAT 1350 Lecture Notes - Lecture 18: Confidence Interval, American Vandal, Netflix
3/20/2018
Chapter 21: Confidence Intervals
● Statistics in the News
○ Headline: “Netflix Survey: Binge-Watching is Not Weird or Unusual”
■ 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
■ If we want to use this information to estimate the population proportion,
we would need to construct a confidence interval
■ N = 3078, ^p = 1876/3078
● Netflix and “Binge-Watching”
○ 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
○ Use the above information to construct a 95% confidence interval ^p = 0.61, n =
3078
■
○ 0.61 +/- (1.960) times the square root of {(.61)(1-.61)}/3078 = 0.61 +/- .018 =
(.592, .628)
○ Interpretation: I am 95% confidence that the population proportion is between
.592 and .628
● More on Netflix and “Binge-Watching
○ We constructed a 95% confidence interval and that interval ended up being from
.592 to .628
○ 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
○ Question: We would expect a 95% confience interval based on a sample of size n
= 60,000 to be what?
■ A. Very wide
■ B. Very narrow
■ C. Not affected since sample size does not impact the width of a
confidence interval
● Go back to formal above ^
● Is a higher confidence level better?
○ Not necessarily
○ Accuracy vs. precision (confidence level relates to accuracy, width of interval
relates to precision)
○ 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
○ 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
● Top at Question
○ A 95% confidence interval is 34% ± 6%. A 90% confidence interval based on this
same sample would have:
■ A. The same center and a larger margin of error.
■ B. The same center and a smaller margin of error.
■ C. A larger margin of error and probably a different center.
■ D. A smaller margin of error and probably a different center.
■ E. The same center, but the margin of error changes randomly.
● Daylight Saving Time
○ Headline: Myths and truths about Daylight Savings Time
■ 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
■ Use this information to construct a 90% confidence interval for the
population proportion