Statistics (2 mc probs)
posted by Joanne .
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 zscores. Which of the following would be true?
a. The mean and the standard deviations of the zscores will be the same as the original data.
b. The mean of the zscores will be zero and the standard deviation will be one.
c. Both the mean and the standard deviation of the zscores 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

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 zscores, the mean of the zdistribution will be zero and the standard deviation will be one.
I hope this will help.