Q1
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.
Q2
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?
We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.
We can estimate with 99% confidence that the sample mean length of adult corn snakes is between 53.88 and 62.12 inches.
We can estimate that 99% of adult corn snakes will have a length that is between 53.88 and 62.12 inches.
Q3
Suppose the germination periods, in days, for grass seed are normally distributed. If the population standard deviation is 3 days, what minimum sample size is needed to be 90% confident that the sample mean is within 1 day of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Q4
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 90% confident that the sample mean is within 5 minutes of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Q5
The weights, in pounds, of dogs in a city are normally distributed with a population standard deviation of 2 pounds and an unknown population mean. A random sample of 16 dogs is taken and results in a sample mean of 28 pounds.
Identify the parameters needed to calculate a confidence interval at the 90% 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.
Q6
The weights, in pounds, of dogs in a city are normally distributed with a population standard deviation of 2 pounds and an unknown population mean. A random sample of 16 dogs is taken and results in a sample mean of 28 pounds.
What is the correct interpretation of the confidence interval?
We can estimate that 90% of the dogs in the city have a weight that lies between 27.18 and 28.82 pounds.
We can estimate with 90% confidence that the sample mean weight of dogs in the city is between 27.18 and 28.82 pounds.
We can estimate with 90% confidence that the true population mean weight of dogs in the city is between 27.18 and 28.82 pounds.
Q7
Suppose the weights, in pounds, of the dogs in a city are normally distributed. If the population standard deviation is 3 pounds, what minimum sample size is needed to be 95% confident that the sample mean is within 1 pound of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer
Q8
Suppose the scores of a standardized test are normally distributed. If the population standard deviation is 4 points, what minimum sample size is needed to be 95% confident that the sample mean is within 1 point of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Solution
Q1
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.
Ans:
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