QUESTION 1

The County Commissioner suspects that the average weekly wage in Cloudy County is lower than the national average of $860. You conduct a simple random sample of 700 adults in Cloudy County and calculate an average weekly wage of $850, with a standard deviation of $47.

Respond to the Commissioner's suspicion by completing the steps below.

1. Write the null and alternative hypotheses
2. What is the appropriate test statistic? Why? Calculate the statistic.
3. What is the degrees of freedom, only if appropriate, and the p-value?
4. Using alpha=.05, should you reject or fail to reject the null hypothesis? Why?
5. State your conclusion directly to the County Commissioner.
6. Are your results practically significant? Explain your answer including a discussion of the magnitude of the results.

QUESTION 2

For reasons beyond your comprehension, the County Commissioner also wonders whether the percent of people who own a pet is different between towns that do and do not have a large park. Luckily, when you collected that sample of 700 adults, you also asked them whether they live in a town with a large park, and whether they own a pet. You calculated the following information:

Among adults in a town with a large park:

Number of adults who own a pet: 112

Sample size: 400

Amount adults in a town without a large park:

Number of adults who own a pet: 78

Sample size: 300

Fulfill the County Commissioner's request by completing the steps below.

1. Write the null and alternative hypotheses.
2. What is the appropriate test statistic? Why? Calculate the statistic.
3. What is the degrees of freedom, if appropriate, and the p-value?
4. Using alpha=.05, should you reject or fail to reject the null hypothesis? Why?
5. State your conclusion directly to the County Commissioner.

QUESTION 3

Using the same sample of 700 adult residents in Cloudy County, the County Commissioner asks you to create an interval estimate(that is, a confidence interval) for the percent of adult residents that support building a dog park. In your sample, 41% of adults support building a dog park.

1. Construct a 93% confidence interval for the proportion supporting building a dog park. Clearly label the standard error and the margin of error. Write the confidence interval formally (i.e., indicate the lower and upper bounds of the interval).
2. Interpret this confidence interval.
3. There is concern that the survey results are biased because of nonresponse. A colleague mentions this is not a concern because the margin of error will capture these sources of bias. Do you agree with this statement? Briefly explain your answer.

QUESTION 4

Using the same sample of 700 adult residents in Cloudy County, the County Commissioner asks you to create an interval estimate(that is, a confidence interval) for the mean household size (i.e. number of people who live in the same household) in the county. In your sample, adults report an average of 3.7 people living in a household, with a standard deviation of 1.2 people. Construct a 99% confidence interval for number of people who live in a household.