Purchase Solution

# Probability Confidence Intervals

Not what you're looking for?

I am currently studying probability and am having a bit of trouble with the following questions. Can you help me? If you can, thank you very much. The questions are:

1.) An office manager wishes to estimate the mean time required to handle customer complaints. A sample of 38 complaints shows a mean time of 28.7 minutes with a standard deviation of 12 minutes.

a) Construct a 90% confidence interval for the true mean time required to handle customer complaints.
b) How large a sample should be taken, if the manager wishes to estimate the mean time to handle a complaint to within +/- one minute? Assume that the confidence interval is to be 90%.

2.) A hospital claims that the average length of stay is 5 days. A study of the length of stay for a random sample of 25 patients found the mean stay to be 6.2 days with a standard deviation of 1.2 days. Do these data present sufficient evidence to support the hospital's claim? Use a 0.05 significance level.

3.) A survey was conducted to determine the proportion of registered nurses in a particular state that are actively employed. A random sample of 400 nurses selected from the state registry showed 274 actively employed. Find a 95% confidence interval estimate for the true proportion of registered nurses actively employed in the state.
Thanks.

##### Solution Summary

This solution provides a step-by-step answer for each of the three probability questions.

##### Solution Preview

1. In part b of the first question, the 90% confidence limits are given by:

28.7 - xm
----------- = +/- 1.645
12/sqrt(38)

where xm = population mean. Thus:

xm = 28.7 +/- 12/sqrt(38)*1.645
= 28.7 +/- 3.20225

And so:

25.498 < xm < 31.902

For question ...

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.