Question

Problem 1: Confidence Interval for Percent of Individuals Vaping (there is no data set)

From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-cigarette) in the past week.

2. Write one sentence each to check the three conditions of the Central Limit Theorem. Show your work for the mathematical check needed to show a large sample size was taken.

4. Verify your result from part (c) using Stat à Proportions Stats à One Sample à With Summary. Inside the box, enter the number of successes, the number of observations, and select confidence interval and click Compute! Copy and paste your StatCrunch result in your document.

Answer 1

b)

Proportion = 248/1186 = 0.209

Conditions for Central Limit Theorem

• Sample size should not be more than 10% of the population. Clearly 1186 is less than 10% of Americans ages 18-29
• Sample size should be large enough for Central Limit Theorem to be applicable. Here it is 1186 which is sufficiently large (greater than 30)
• Also, both n*p and (1-n)*p should be greater than 10. Here that is also true.

d)

Part c is missing, hence cannot verify.

Though,

n*p = 0.209*1186 = 248 > 10

and n*(1-p) = 1186*(1-0.209) = 938 > 10