Confidence Intervals

During the recent recovery from the Great Recession of 2007-2009, the economic situation for many families has improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national level. To estimate the population parameter of the percent of lowincome working families, a representative simple random sample could be used to calculate a point estimate and a confidence interval.

7. Write an appropriate sampling procedure that will enable a researcher to collect a simple random sample of size n=20 from the full list of jurisdictions.

8. Carry out a sampling of the jurisdictions by using a random number generator, random number table, or the sampling capabilities of technology to select a simple random sample of size n=20 from the full list of the jurisdictions. Provide the selected sample of 20 in the table included below, making sure to include the corresponding percent of low-income working families (%LIWF) information for each jurisdiction selected.

Jurisdiction %LIWF Jurisdiction %LIWF Jurisdiction %LIWF Jurisdiction %LIWF

9. Use technology to calculate the sample mean and sample standard deviation of the percent of low-income working families for the selected 20 jurisdictions in your sample. Provide your mean and standard deviation and express in detail why it is unlikely that any two samples would produce the same results.

10. A different sample of size n=20 produced a sample mean of 31.08% and a sample standard deviation of 5.48%. Use these values to calculate a 90% confidence interval (without the use of statistical technology) for the national mean percent of low-income working families. Please show all calculations and provide the upper and lower limits that make up the confidence interval. (Round the limits to two decimal places.)

11. Express an appropriate statistical interpretation of the 90% confidence interval included in the answer to number 10.

12. In any of the 20-value samples selected, some jurisdictions may have a percent of low-income working families that is not included in the 90% confidence interval calculated above. If federal funds are available only for jurisdictions whose percent of low-income working families falls within the reported confidence interval, explain whether an interval with a higher or lower confidence level would be more advantageous to the jurisdictions.

13. If a lawmaker reports only research results that ensure that the jurisdiction he or she represents gets federal aid, explain whether such an action would constitute a misuse of statistics. If the action is not a misuse, state why it is appropriate. If the action is a misuse, state an alternate reporting practice that would be more appropriate.

Rev 10/ 2016

Hypothesis Testing

In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% (The Working Poor Families Project, 2011). Although it has remained slow, some politicians now claim that the recovery from the Great Recession has been steady and noticeable. As a result, it is believed that the national percent of low-income working families is significantly lower now in 2014 than it was in 2011. To support this belief, a recent spring 2014 sample of n=16 jurisdictions produced a sample mean of 29.8% for the percent of low income working families, with a sample standard deviation of 4.1%. Using a 0.10 significance level, test the claim that the national average percent of low-income working families has improved since 2011.

14. Write a few brief sentences to state the type of test that should be performed and state the assumptions and conditions that justify its appropriateness.

15. Clearly identify and state the null and alternate hypothesis for this test.

16. Use technology to identify the test statistic and the P-value associated with the hypothesis test. Provide these values.

17. State the decision of the hypothesis test based on a 0.10 significance level.

18. Provide the appropriate conclusion about the claim that the national average percent of low income working families has improved since 2011.