Question

I have the following two multiple choice questions that are really throwing me for a loop:

1. Based on 500 people a researcher calculates the 95% confidence interval for the population proportion p: 0.123<p<0.181.
a. There is a 95% chance that the true value of p lies between 0.113 and 0.171.
b. If many diff. samples of 300 were selected and a confidence interval was constructed based on that sample, in the long run, 95% of the confidence intervals would contain the true value of p.
c. If 100 different samples of 300 were selected and a confidence interval was constructed based each sample, exactly 99 of these confidence intervals contain the true value of p.

---In all honesty, none of these answers feels right, any thoughts?


2. Suppose all values in a data set are converted to z-scores. Which of the following would be true?
a. The mean and the standard deviations of the z-scores will be the same as the original data.
b. The mean of the z-scores will be zero and the standard deviation will be one.
c. Both the mean and the standard deviation of the z-scores will be zero.

---My instinct on this question is a, just because it is the only one that makes some sense. What do you think?

Thank you,
Joanne

Answer 1

With a 95% confidence interval, one can be 95% confident that the true value of p is contained within that interval.

If you calculate the mean and standard deviation of the z-scores, the mean of the z-distribution will be zero and the standard deviation will be one.

I hope this will help.