Mystic Falls Confidence Interval
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- Горка: 1
- Did you hear Mr. Saltzman talk about the history of vampires in Mystic Falls? Do you think they really exist?
- Well, I've heard some rumors... Let's get some data to see.
- Горка: 2
- Damon?! You're a vampire?
- Горка: 3
- I can't believe this. You and your brother are some of the vampires of this town.
- Its okay, lets focus on the data we gathered.
- Горка: 4
- In Mystic Falls, there have been rumors about the population makeup, particularly the proportion of vampires to humans. To investigate this, a sample of 200 individuals was taken, and it was found that 35 of them were vampires.
- Now lets Compute a 95% confidence interval for the true proportion of vampires to humans in Mystic Falls based on this sample.
- Горка: 5
- Great! Now we need to use the formula for a confidence interval for a proportion
- The sample proportion of vampires in Mystic Falls is calculated as:Sample Proportion = Number of Vampires/Total Sample SizeSo, in this case:Sample Proportion = 35/200 = 0.175
- Горка: 6
- Let's use this formula and plug in all of the necessary values
- Горка: 7
- This gives us the confidence interval as (0.122,0.227)
- For a 95% confidence level, 𝑍 = 1.960Plugging in the values:Confidence Interval = 0.175 ± 1.960 × √(0.175 × 0.825) / 200 Confidence Interval = 0.175 ± 0.0527
- Горка: 8
- We are 95% confident that the true proportion of vampires to humans in Mystic Falls lies between 0.122 and 0.227. This means that based on our sample, we estimate that anywhere from approximately 13.2% to 21.8% of the population in Mystic Falls are vampires.
- Great work. AHHHH a vampire!
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