Question

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.

Answer & Explanation
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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

 

xˉE<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.)

 

sE<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.)

 

xˉE<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.)

 

xˉE<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

 

sample statistic=2upper limit+lower limit

 

sample statistic=0.049

 

 

The formula for calculating the margin of error is

 

margin of error=2upper limitlower limit

 

margin of error=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

 

sample statistic=2upperlimit+lowerlimit

 

sample statistic=0.0755

 

 

The formula for calculating the margin of error is

 

margin of error=2upper limitlower limit

 

margin of error=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

 

sample statistic=2upperlimit+lowerlimit

 

sample statistic=2.605

 

 

The formula for calculating the margin of error is

 

margin of error=2upper limitlower limit

 

margin of error=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.

Step-by-step explanation

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

 

xˉE<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

 

4.91.3<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.)

 

sE<σ<s+E

 

17.113.31<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.)

 

xˉE<μ<xˉ+E

 

15.983.78<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.)

 

xˉE<μ<xˉ+E

 

172.5511.272<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

 

sample statistic=2upper limit+lower limit

 

sample statistic=20.052+0.046

 

sample statistic=0.049

 

 

The formula for calculating the margin of error is

 

margin of error=2upper limitlower limit

 

margin of error=20.0520.046

 

margin of error=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

 

sample statistic=2upperlimit+lowerlimit

 

sample statistic=20.083+0.068

 

sample statistic=0.0755

 

 

The formula for calculating the margin of error is

 

margin of error=2upper limitlower limit

 

margin of error=20.0830.068

 

margin of error=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

 

sample statistic=2upperlimit+lowerlimit

 

sample statistic=22.87+2.34

 

sample statistic=2.605

 

 

The formula for calculating the margin of error is

 

margin of error=2upper limitlower limit

 

margin of error=22.872.34

 

margin of error=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.