Question

A student was asked to find a 90% confidence interval for widget width using data from a random sample of size n = 23.

Which of the following is a correct interpretation of the interval 13.5 < μ < 33.5?

Check all that are correct.

• There is a 90% chance that the mean of the population is between 13.5 and 33.5.
• With 90% confidence, the mean width of a randomly selected widget will be between 13.5 and 33.5.
• There is a 90% chance that the mean of a sample of 23 widgets will be between 13.5 and 33.5.
• With 90% confidence, the mean width of all widgets is between 13.5 and 33.5.
• The mean width of all widgets is between 13.5 and 33.5, 90% of the time. We know this is true because the mean of our sample is between 13.5 and 33.5.

Answer 1

Before selecting the options lets explain what does Confidence Interval means-

90% CI means it is 90% certain that the given confidence intervals contains the true population parameter. Here the mean is the parameter. We need to do experiment repeatedly to say that 90% of the times the CI is containing that population parameter. For doing this we always take fixed number of samples and find the CI.

So here sample size is 23 and the CI is (13.5,33.5)

So the options are

The mean width of all widgets is between 13.5 and 33.5, 90% of the time. We know this is true because the mean of our sample is between 13.5 and 33.5.

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