1. Learn
    2. /
  2. Courses
    3. /
  3. HarvardX Data Science Module 4 - Inference and Modeling

Exercise

Exercise 15 - Calculate the 95% Confidence Interval of the Spreads

We have constructed a random variable that has expected value \(b_2 - b_1\), the pollster bias difference. If our model holds, then this random variable has an approximately normal distribution. The standard error of this random variable depends on \(\sigma_1\) and \(\sigma_2\), but we can use the sample standard deviations we computed earlier. We have everything we need to answer our initial question: is \(b_2 - b_1\) different from 0?

Construct a 95% confidence interval for the difference \(b_2\) and \(b_1\). Does this interval contain zero?

Instructions

100 XP
  • Use pipes %>% to pass the data polls on to functions that will group by pollster and summarize the average spread, standard deviation, and number of polls per pollster.
  • Calculate the estimate by subtracting the average spreads. Save this estimate to a variable called estimate.
  • Calculate the standard error using the standard deviations of the spreads and the sample size. Save this value to a variable called se_hat.
  • Calculate the 95% confidence intervals using the qnorm function. Save the lower and then the upper confidence interval to a variable called ci.