Question

A scientist is about to collect data to compute a 95% confidence interval, but he is unsure of what a 95% confidence interval really means. Help him out by filling in the blanks. Before a sample is chosen, there is a 95% ______________ that the sample will produce an interval containing the true mean value. After a sample has been chosen, there is 95% ________________ that the interval produced by the sample will contain the true mean value.

a. probability/probability

b. confidence/confidence

c. confidence/probability

d. probability/chance

e. probability/confidence

Answer 1

c. confidence/probability

Explanation:

The margin of error of a confidence interval is:

M = T*s.

In which T is related to the confidence level and s is the standard deviation of the sample.

In which

z is the zscore that has a pvalue of
`1 - (\alpha)/(2)`.

Before the sample is chosen

We choose our confidence level, which will determine the value of T. So the first answer is confidence.

After the sample is chosen

We are 95% sure that the true mean is in the sample. So the second answer is probability.

So the correct answer is:

c. confidence/probability