Problem Set Section 2E Directions: Answer the following questions.

1. What are the assumptions necessary for making a one-population proportion confidence interval?

2. What are the assumptions necessary for making a one-population mean confidence interval?

3. What are the assumptions necessary for making a one-population bootstrap confidence interval?

4. An experiment was conducted to see what percentage of rats would show empathy toward fellow rats in distress. Of the 30 total rats in the study, 23 showed empathy. What was the sample proportion? What are the critical value Z-scores for 99% confidence? If you cannot remember them, open StatKey at www.lock5stat.com. Go to “theoretical distributions” and click on “normal”. You can look up the critical value Z-scores. Use the critical values and the given standard error to calculate the margin of error and construct a 99% confidence interval estimate of the population proportion of rats that show empathy. Convert the upper and lower limits of your confidence interval into percentages.

Standard Error ? 0.07725

a) Sample Proportion ????? = ???????????????????????? ???????? ???????????????????????????? (????????????????????????) ???????????????????? ???????????????????????? ????????????????

=

b) Critical value Z-scores = ±

c) Margin of Error = ????× ???????????????????????????????? ???????????????????? =

d) Confidence Interval Lower Limit = ????? ? (???????????????????????? ???????? ????????????????????)

e) Confidence Interval Upper Limit = ????? + (???????????????????????? ???????? ????????????????????)

5. Use the following Statcato printout to check your margin of error and confidence interval answers from the rat empathy data in number 4. Now check the assumptions and write sentences to explain the margin of error and confidence interval.

a) Check each of the assumptions for this problem. Assume the rats were randomly selected. Explain your answers.

b) Write a sentence to explain the margin of error in context.

c) Write a sentence to explain the confidence interval in context.

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