Q1. Suppose a sample of 10,001 erroneous Federal income tax returns from last year has been taken and is provided in the Excel File Week 8 Data.xlsx sheet FedTaxErrors. A positive value indicates the taxpayer underpaid and a negative value indicates that the taxpayer overpaid.

What is the sample mean error made on erroneous Federal income tax returns last year?

Using 95% confidence, what is the margin of error?

Using the results from parts (a) and (b), develop the 95% confidence interval estimate of the mean error made on erroneous Federal income tax returns last year.

Q2. According to the Census Bureau, 2,475,780 people are employed by the federal government in the United States. Suppose that a random sample of 3,500 of these federal employees was selected and the number of sick hours each of these employees took last year was collected from an electronic personnel database. The data collected in this survey are provided in the sheet Excel File Week 8 Data.xlsx sheet FedSickHours.

What is the sample mean number of sick hours taken by federal employees last year?

Using 99% confidence, what is the margin of error?

Using the results from parts (a) and (b), develop the 99% confidence interval estimate of the mean number of sick hours taken by federal employees last year.

If the mean sick hours federal employees took two years ago was 62.2, what would

the confidence interval in part (c) lead you to conclude about last year?

Q3. One of the questions on a survey of 1,000 adults asked if todays children will be better off than their parents. Representative data are shown in the sheet named ChildOutlook in Excel File Week 8 Data.xlsx. A response of Yes indicates that the adult surveyed did think todays children will be better off than their parents. A response of No indicates that the adult surveyed did not think todays children will be better off than their parents. A response of Not Sure was given by 23% of the adults surveyed.

What is the point estimate of the proportion of the population of adults who do think that todays children will be better off than their parents?

At 95% confidence, what is the margin of error?

What is the 95% confidence interval for the proportion of adults who do think that todays children will be better off than their parents?

What is the 95% confidence interval for the proportion of adults who do not think that todays children will be better off than their parents?

Which of the confidence intervals in parts (c) and (d) has the smaller margin of error? Why?

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