Confidence Intervals

Question

A recent poll stated that out of the 40 people interviewed, 22 of them drove to work. Create a 95% confidence interval for the true percentage of people who drive to work. Assume the data are normally distributed and build a confidence interval

Answer 1

Confidence Interval = p-hat ± Z * √(p-hat * (1 - p-hat) / n)

Where:

1. Z is the critical value from the standard normal distribution for a 95% confidence level. For 95%, Z ≈ 1.96
2. p-hat is the sample proportion, which is 0.55 (22 out of the 40 people interviewed drove to work)
3. n is the sample size, which is 40

After substituting in the values and calculating, the confidence interval in percentages is: 39.58% to 70.42%. This means that we are 95% confident that the true proportion of people who drive to work lies within this range.

Hope this was helpful.