Question

A sample of size 42 college students produced a 95% confidence interval of (3.1, 5.2) for the mean number of coats owned. Then there is a 95% chance that these 42 students own on average between 3.1 and 5.2 coats.

a. True
b. False

Answer 1

The statement is False. A 95% confidence interval does not represent a probability of the sample mean falling within that interval. It represents the percentage of confidence intervals from repeated sampling that would contain the true population mean.

Step-by-step explanation:

The statement is False. A 95% confidence interval means that if we were to take repeated samples from the population and construct 95% confidence intervals, approximately 95% of those intervals would contain the true population mean.

In this case, the confidence interval (3.1, 5.2) means that we are 95% confident that the true mean number of coats owned by all college students is between 3.1 and 5.2 coats, based on the sample of 42 students.

It does not mean that there is a 95% chance that these 42 students own on average between 3.1 and 5.2 coats.

Answer 2

b. False.

Step-by-step explanation:

According to the presented information, at the 95% confidence level, the mean number of coats owned will be between 3.1 and 5.2. That does not mean that there is a 95% chance that they will own that many coats; just that you are 95% confident that they will own the coats.

Hope this helps!