QUESTIONS
Question 1
Suppose the number of dollars spent per week on groceries is normally distributed. If the population standard deviation is 7 dollars, what minimum sample size is needed to be 90% confident that the sample mean is within 3 dollars of the true population mean?
| Z0.10 | Z0.05 | Z0.025 | Z0.01 | Z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Use the table above for the z-score, and be sure to round up to the next integer.
= (1.645)2(7)2 / 32
Question 2
Suppose the number of defects in a sweater from a population of sweaters produced from a textile factory are normally distributed with an unknown population mean and a population standard deviation of 0.06 defects. A random sample of sweaters from the population produces a sample mean of x¯=1.3 defects.
What value of z should be used to calculate a confidence interval with a 95% confidence level?
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Question 3
The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches.
What is the correct interpretation of the confidence interval?
Question 4
The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches.
Identify the parameters needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.
| z0.10z0.10 | z0.05z0.05 | z0.025z0.025 | z0.01z0.01 | z0.005z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
You may use a calculator or the common z values above.
- Round the final answer to two decimal places.
x = 1
σ = 2
n = 3
zα/2 = 4
(5, 6)
Question 5
Suppose the number of free throws in a basketball game by one player are normally distributed with a standard deviation 0.97 free throws. A random sample of basketball players from the population produces a sample mean of x¯=4.9 free throws.
What value of z should be used to calculate a confidence interval with a 95% confidence level?
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Question 6
The population standard deviation for the total snowfalls per year in a city is 13 inches. If we want to be 95% confident that the sample mean is within 3 inches of the true population mean, what is the minimum sample size that should be taken?
| Z0.10 | Z0.05 | Z0.025 | Z0.01 | Z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Use the table above for the z-score, and be sure to round up to the next integer.
Question 7
The weekly salaries of sociologists in the United States are normally distributed and have a known population standard deviation of 425 dollars and an unknown population mean. A random sample of 22 sociologists is taken and gives a sample mean of 1520 dollars.
Find the margin of error for the confidence interval for the population mean with a 98% confidence level.
| z0.10z | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
You may use a calculator or the common z values above.
- Round the final answer to two decimal places.
Question 8
A bank offers auto loans to qualified customers. The amount of the loans are normally distributed and have a known population standard deviation of 4 thousand dollars and an unknown population mean. A random sample of 22 loans is taken and gives a sample mean of 42 thousand dollars.
Find the margin of error for the confidence interval for the population mean with a 90% confidence level.
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
You may use a calculator or the common z values above.
- Round the final answer to two decimal places.
Question 9
Suppose heights of seasonal pine saplings are normally distributed and have a known population standard deviation of 17 millimeters and an unknown population mean. A random sample of 15 saplings is taken and gives a sample mean of 308 millimeters.
Find the confidence interval for the population mean with a 90% confidence level.
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
You may use a calculator or the common z values above.
- Round the final answer to two decimal places.
Question 10
The number of square feet per house are normally distributed with a population standard deviation of 197 square feet and an unknown population mean. If a random sample of 25 houses is taken and results in a sample mean of 1820 square feet, find a 99% confidence interval for the population mean.
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
You may use a calculator or the common z values above.
- Round the final answer to one decimal place.
Question 11
In a recent survey, a random sample of 130 families were asked about whether they have a pet, and 67 reported that they have a pet.
What value of z should be used to calculate a confidence interval with a 90% confidence level?
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Question 12
Suppose the heights of a population of male giraffes are normally distributed with an unknown population mean and a population standard deviation of 3.4 feet. A random sample of male giraffes from the population produces a sample mean height of x¯=15.2 feet.
What value of z should be used to calculate a confidence interval with a 90% confidence level?
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Question 13
Suppose the speeds of vehicles traveling on a highway are normally distributed and have a known population standard deviation of 7 miles per hour and an unknown population mean. A random sample of 32 vehicles is taken and gives a sample mean of 64 miles per hour.
Find the margin of error for the confidence interval for the population mean with a 98% confidence level.
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
You may use a calculator or the common z values above.
- Round the final answer to two decimal places.
Question 14
The number of hours that a nine month old baby sleeps at night are normally distributed with a population standard deviation of 1.5 hours and an unknown population mean. A random sample of 22 nine month old babies is taken and results in a sample mean of 12 hours.
Find the margin of error for a confidence interval for the population mean with a 90% confidence level.
| z0.10z0.10 | z0.05z0.05 | z0.025z0.025 | z0.01z0.01 | z0.005z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
You may use a calculator or the common z values above.
- Round the final answer to two decimal places.
Question 15
The population standard deviation for the scores of a standardized test is 5 points. If we want to be 95% confident that the sample mean is within 2 points of the true population mean, what is the minimum sample size that should be taken?
| Z0.10 | Z0.05 | Z0.025 | Z0.01 | Z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Use the table above for the z-score, and be sure to round up to the next integer.
Question 16
Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 95% confident that the sample mean is within 5 minutes of the true population mean?
| Z0.010 | Z0.005 | Z0.025 | Z0.01 | Z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Use the table above for the z-score, and be sure to round up to the next integer.
ANSWERS:
Question 1
Suppose the number of dollars spent per week on groceries is normally distributed. If the population standard deviation is 7 dollars, what minimum sample size is needed to be 90% confident that the sample mean is within 3 dollars of the true population mean?
| Z0.10 | Z0.05 | Z0.025 | Z0.01 | Z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Use the table above for the z-score, and be sure to round up to the next integer.
Answer
15 grocery totals
Question 2
Suppose the number of defects in a sweater from a population of sweaters produced from a textile factory are normally distributed with an unknown population mean and a population standard deviation of 0.06 defects. A random sample of sweaters from the population produces a sample mean of x¯=1.3 defects.
What value of z should be used to calculate a confidence interval with a 95% confidence level?
| z0.10 | z0.05 | z0.025 | z0.01 | z0.005 |
| 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Answer
1.960
Question 3
The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches.
What is the correct interpretation of the confidence interval?
Answer
We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.
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