# 1. "What is the population percent of the adult population is infected

with this disease?" Sample percentage = 4.9% Margin of error = 1.3% (Found with 95% confidence level.)

3. What is the population standard deviation for the systolic blood pressure in women? (Assume there was a normal sampling distribution.) Sample standard deviation = 17.11 mm of Hg Margin of error = 3.31 mm of Hg (Found with 90% confidence level.)

5. What is the population mean average price of a used mustang car in thousands of dollars? Sample mean = 15.98 thousand dollars Margin of error = 3.78 thousand dollars (Found with 90% confidence level.)

7. "What is the population mean average weight for men?" Sample mean = 172.55 pounds Margin of error = 11.272 pounds (Found with 99% confidence level.)

11. A 95% confidence interval estimate of the population proportion of fat in the milk from Jersey cows is (0.046 , 0.052).

13. A 90% confidence interval estimate of the population proportion of people who will vote for the Independent party candidate is 0.068 < π < 0.083.

15. A 99% confidence interval estimate of the population standard deviation for the height of men in inches is 2.34 < σ < 2.87. Assume there was a normal sampling distribution.

26. Here is the definition of 95% confidence: "95% of confidence intervals contain the population parameter and 5% do not contain the population parameter". Explain this definition of 95% confidence.

*Answers:*

The confidence interval for the population proportion is given by

$p^ −E<p<p^ +E$

Where:

$p^ $: sample proportion (point estimate)

$E$: margin of error

The confidence interval for the population mean is given by

$xˉ−E<μ<xˉ+E$

Where:

$xˉ$: sample mean (point estimate)

$E$: margin of error

**1. "What is the population percent of the adult population is infected with this disease?" Sample percentage = 4.9% Margin of error = 1.3% (Found with 95% confidence level)**

$p^ −E<p<p^ +E$

$3.6<p<6.2$

$CI=(3.6,6.2)$

We are 95% confident that the true population percent of the adult population is infected with this disease between 3.6% and 6.2%.

**3. What is the population standard deviation for the systolic blood pressure in women? (Assume there was a normal sampling distribution.) Sample standard deviation = 17.11 mm of Hg Margin of error = 3.31 mm of Hg (Found with 90% confidence level.)**

$s−E<σ<s+E$

$13.80<σ<20.42$

$CI=(13.80,20.42)$

We are 90% confident that the true population standard deviation for the systolic blood pressure in women is between 13.80 mm of Hg and 20.42 mm of Hg.

**5. What is the population mean average price of a used mustang car in thousands of dollars? Sample mean = 15.98 thousand dollars Margin of error = 3.78 thousand dollars (Found with 90% confidence level.)**

$xˉ−E<μ<xˉ+E$

$12.20<μ<19.76$

$CI=(12.20,19.76)$

We are 90% confident that the true population mean average price of a used mustang car in thousands of dollars is between 12.20 and 19.76.

**7. "What is the population mean average weight for men?" Sample mean = 172.55 pounds Margin of error = 11.272 pounds (Found with 99% confidence level.)**

$xˉ−E<μ<xˉ+E$

$161.278<μ<183.822$

$CI=(161.278,183.822)$

We are 99% confident that the true population mean average weight for men is between 161.278 pound and 183.822 pounds.

**11. A 95% confidence interval estimate of the population proportion of fat in the milk from Jersey cows is (0.046 , 0.052).**

We are 95% confident that the true population proportion of fat in the milk from Jersey cows is between 0.046 and 0.052

The sample statistic is $p^ $. The formula for calculating the sample statistic is

$samplestatistic=2upperlimit+lowerlimit $

$samplestatistic=0.049$

The formula for calculating the margin of error is

$marginoferror=2upperlimit−lowerlimit $

$marginoferror=0.003$

**13. A 90% confidence interval estimate of the population proportion of people who will vote for the Independent party candidate is 0.068 < π < 0.083**

We are 90% confident that the true population proportion of people who will vote for the Independent party candidate is between 0.068 and 0.083

The sample statistic is $p^ $. The formula for calculating the sample statistic is

$samplestatistic=2upperlimit+lowerlimit $

$samplestatistic=0.0755$

The formula for calculating the margin of error is

$marginoferror=2upperlimit−lowerlimit $

$marginoferror=0.0075$

**15. A 99% confidence interval estimate of the population standard deviation for the height of men in inches is 2.34 < σ < 2.87. Assume there was a normal sampling distribution.**

We are 99% confident that the true population standard deviation for the height of men in inches is between 2.34 and 2.87

The sample statistic is $s$. The formula for calculating the sample statistic is

$samplestatistic=2upperlimit+lowerlimit $

$samplestatistic=2.605$

The formula for calculating the margin of error is

$marginoferror=2upperlimit−lowerlimit $

$marginoferror=0.265$

**26. Here is the definition of 95% confidence: "95% of confidence intervals contain the population parameter and 5% do not contain the population parameter". Explain this definition of 95% confidence. **

This definition of 95% confidence interval means that 95% of the time, the interval will contain the population parameter (population mean, population proportion, population standard deviation). Therefore, we are 95% confident that the population parameter is within the interval.

The confidence interval for the population proportion is given by

$p^ −E<p<p^ +E$

Where:

$p^ $: sample proportion (point estimate)

$E$: margin of error

The confidence interval for the population mean is given by

$xˉ−E<μ<xˉ+E$

Where:

$xˉ$: sample mean (point estimate)

$E$: margin of error

**1. "What is the population percent of the adult population is infected with this disease?" Sample percentage = 4.9% Margin of error = 1.3% (Found with 95% confidence level)**

$p^ −E<p<p^ +E$

$4.9−1.3<p<4.9+1.3$

$3.6<p<6.2$

$CI=(3.6,6.2)$

We are 95% confident that the true population percent of the adult population is infected with this disease between 3.6% and 6.2%.

**3. What is the population standard deviation for the systolic blood pressure in women? (Assume there was a normal sampling distribution.) Sample standard deviation = 17.11 mm of Hg Margin of error = 3.31 mm of Hg (Found with 90% confidence level.)**

$s−E<σ<s+E$

$17.11−3.31<σ<17.11+3.31$

$13.80<σ<20.42$

$CI=(13.80,20.42)$

We are 90% confident that the true population standard deviation for the systolic blood pressure in women is between 13.80 mm of Hg and 20.42 mm of Hg.

**5. What is the population mean average price of a used mustang car in thousands of dollars? Sample mean = 15.98 thousand dollars Margin of error = 3.78 thousand dollars (Found with 90% confidence level.)**

$xˉ−E<μ<xˉ+E$

$15.98−3.78<μ<15.98+3.78$

$12.20<μ<19.76$

$CI=(12.20,19.76)$

We are 90% confident that the true population mean average price of a used mustang car in thousands of dollars is between 12.20 and 19.76.

**7. "What is the population mean average weight for men?" Sample mean = 172.55 pounds Margin of error = 11.272 pounds (Found with 99% confidence level.)**

$xˉ−E<μ<xˉ+E$

$172.55−11.272<μ<172.55+11.272$

$161.278<μ<183.822$

$CI=(161.278,183.822)$

We are 99% confident that the true population mean average weight for men is between 161.278 pound and 183.822 pounds.

**11. A 95% confidence interval estimate of the population proportion of fat in the milk from Jersey cows is (0.046 , 0.052).**

We are 95% confident that the true population proportion of fat in the milk from Jersey cows is between 0.046 and 0.052

The sample statistic is $p^ $. The formula for calculating the sample statistic is

$samplestatistic=2upperlimit+lowerlimit $

$samplestatistic=20.052+0.046 $

$samplestatistic=0.049$

The formula for calculating the margin of error is

$marginoferror=2upperlimit−lowerlimit $

$marginoferror=20.052−0.046 $

$marginoferror=0.003$

**13. A 90% confidence interval estimate of the population proportion of people who will vote for the Independent party candidate is 0.068 < π < 0.083**

We are 90% confident that the true population proportion of people who will vote for the Independent party candidate is between 0.068 and 0.083

The sample statistic is $p^ $. The formula for calculating the sample statistic is

$samplestatistic=2upperlimit+lowerlimit $

$samplestatistic=20.083+0.068 $

$samplestatistic=0.0755$

The formula for calculating the margin of error is

$marginoferror=2upperlimit−lowerlimit $

$marginoferror=20.083−0.068 $

$marginoferror=0.0075$

**15. A 99% confidence interval estimate of the population standard deviation for the height of men in inches is 2.34 < σ < 2.87. Assume there was a normal sampling distribution.**

We are 99% confident that the true population standard deviation for the height of men in inches is between 2.34 and 2.87

The sample statistic is $s$. The formula for calculating the sample statistic is

$samplestatistic=2upperlimit+lowerlimit $

$samplestatistic=22.87+2.34 $

$samplestatistic=2.605$

The formula for calculating the margin of error is

$marginoferror=2upperlimit−lowerlimit $

$marginoferror=22.87−2.34 $

$marginoferror=0.265$

**26. Here is the definition of 95% confidence: "95% of confidence intervals contain the population parameter and 5% do not contain the population parameter". Explain this definition of 95% confidence. **

This definition of 95% confidence interval means that 95% of the time, the interval will contain the population parameter (population mean, population proportion, population standard deviation). Therefore, we are 95% confident that the population parameter is within the interval.