Statistic

Complete the problems below. Show some of your steps and explain the answer, too. If you use StatCrunch to compute a confidence interval, shot a screenshot of your output, or type out your input (so your work can be error-checked).

Question #1

A 95% confidence interval for a population proportion yielded the interval (.345, .455). (This is enough information to answer the following questions. Don’t over-think these questions!)

1. Compute the margin of error.

1. Compute the sample proportion.

2. Will a 90% confidence interval be wider or narrower? Explain.

Question #2

Many companies are interested in knowing the percentage of adults who buy clothing online. How many adults must be surveyed in order to be 95% confident that the sample percentage is in error by no more than three percentage points?

1. Use a recent result from the Census Bureau:  70% of adults buy clothing online.

1. Assume that we have no prior information suggesting a possible value of the proportion.

Question #3

A Pew Research Center poll of 1007 randomly selected adults showed that 42% of those survey feel the Internet is a bad influence on morality.  

1. What is the value of n? pˆ?

2. Compute the margin of error E that corresponds to a 95% confidence level.

3. Compute the 95% confidence interval estimate of the population proportion p.

4. Based on the results, can we safely conclude that more than half of adults feel the Internet is a bad influence on morality?

5. Assuming that you are a newspaper reporter, write a brief statement that accurately describes the results and includes all of the relevant information.