Kimberly, who is the TA for an introductory statistics course, isgrading respons

Question

Kimberly, who is the TA for an introductory statistics course, isgrading responses to a question that asks the students to interpreta confidence interval.

Here is the question:

Suppose we want to estimate the mean credit card debt for studentsat a college with an enrollment of about 5000 students. We select arandom sample of 250 students and find that their average debt isabout $3000.00 with a standard deviation of $500.00. We use thesample statistic and construct the 95% confidence interval from$2938.00 to $3062.00

Here are three inaccurate responses:

1. If we choose one hundred random samples of size 250 from thispopulation and calculate the 95% confidence interval, in 95 out of100 cases the average amount of credit card debt will be between$2938.00 to $3062.00
2. We are 95% confident that the average credit card debt for thissample is between $2938.00 to $3062.00
3. There is a 95% chance that the average credit card debt forthis population will be between $2938.00 to $3062.00 and there is a5% chance that it will not.

Question to be answered:

Choose one of the three responses and EXPLAIN EXPLICITLY why youthink that the interpretation is in accurate.

Explanation / Answer

We are 95% confident that the average credit card debt forthis sample is between $2938.00 to $3062.00
I was always taught thatconfidence do what they say, they state how confident you are ofsomething. When explaining a confidence interval, you alwaysstart by saying you are blank percent confident that blank is true.
I am not good at explaining thisbut I know that this is the correct response.

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