The St. Lucie County Health Department needs to estimate the proportion of all children in the county aged 19-35 months that are completely up to date with all state-recommended immunizations. The St. Lucie County Health department fund that 86% of a random sample of children in the county aged 19-35 months were completely up to date with all state recommended immunizations.

Find three different confidence intervals-one with sample size 378, one with sample size 731, and one with sample size 907. Assume that 86% of the children each sample are completely up to date with all state-recommended immunizations. Notice how the sample size affects the margin of error and the width of the interval.

Report confidence interval solutions using interval notation. Report all solution in percent form, rounded to two decimal places, if necessary.

- When n = 378, the margin of error for a 96% confidence interval is given by =-----

When n = 378, a 96% confidence interval is given by =----

- When n = 731, the margin of error for a 96% confidence interval is given by =----

When n = 731, a 96% confidence interval is given by = ----

- When n = 907, the margin of error for a 96% confidence interval is given by = -----

When n = 907, a 96% confidence interval is given by =-----

2- A campaign staffer would like to estimate the proportion of likely voters who will vote for a particular candidate in the upcoming election. To help with this estimate, the staffer surveyed a small group of likely voters and found that 93% of the sample supported the candidate.

How large a sample should be selected such that the margin of error of the estimate for a 95% confidence interval is at most 5.2%. Round the solution up to the nearest whole number.

n =

3- A local non-profit group would like to estimate the proportion of residents of Indian River county who do not have health insurance.

Determine the most sample size required to limit the margin of error to within 0.041 of the population proportion for a 95% confidence interval. Round the solution up to the nearest whole number.

n=

4-An economist needs to estimate the proportion of residents of Port St. Lucie that have earned a college degree. Determine the most conservative estimate of the sample size required to limit the margin of error to within 0.043 of the population proportion for a 90% confidence interval.

Round the solution up to the nearest whole number.

n =

5- A marine biologist would like to estimate the mean weight of all kingfish on the treasure Coast, using a 96% confidence interval. The standard deviation of the weight of all kingfish on the treasure coast is known to be 7.8 pounds. How large a sample of kingfish should the marine biologist select so that the estimate is within 1.26 pounds of the true population mean. Round the solution up to the nearest whole number.

n =---

6- A city official would like to estimate the mean of all residents of Stuart. The standard deviation of the ages of all residents of Stuart is known to be 20 years. Determine the sample size necessary such that the margin of error of the estimate for a 95% confidence interval for the mean age of all residents is at most 3.4 years. Round the solution up to the nearest whole number.

n = ----