Question

0. Confidence intervals occur in our daily lives more than most people realize. For instance, you may not know how much money is in your pocket down to the penny, but you do know if it's between $1 and $100. [That's an informal example of a confidence interval that’s not exactly accurate but gets at the intuition of what a confidence interval is.]

Can you come up with a similar example from daily life in which you think in confidence intervals?

1. Here is an example of an actual margin of error. How can we translate this into the language of confidence intervals at the 95% confidence level:

According to a Gallup poll in 2017, 43% of Americans approved of the job the president was doing, with a margin of error of 3 percentage points.

Answer 1

0)

Confidence Interval (example)

Let a student needs to consume 2500 calories per day to maintain good health but when we record the daily calorie intake for a student it varies with certain mean and standard deviation. Hence a confidence interval can be used to determine the daily intake of the student.

1)

The point estimate of the proportion, p = 0.43

The Margin of Error (ME) = 0.03

95% CI = [p - ME, p + ME)

95% CI = [0.43 - 0.03, 0.43 + 0.03]

95% CI = [0.40, 0.46]

Interpretation: There is a 95% chance that the true population proportion of Americans who approved of the job the president was doing lies in the interval of 40% to 46%.