8.1c Confidence Interval for Population Mean- Population Standard Deviation Known

Suppose the weights of running shoes are normally distributed with a population standard deviation of 5 ounces and an unknown population mean. A random sample of 29 running shoes is taken, which results in a sample mean of 23 ounces. Find the margin of error for the confidence interval with a 90% confidence level. z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.

Margin of Error: 1.53

The ages of millionaires in a city are normally distributed with a population standard deviation of 3 years and an unknown population mean. A random sample of 23 millionaires is taken and results in a sample mean of 44 years. Find the margin of error for a 95% confidence interval for the population mean. z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.

Margin of error = 1.23

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 = 1.282 z0.05 = 1.645 z0.025 = 1.960 z0.01 = 2.326 z0.005 = 2.576 You may use a calculator or the common z values above. Use 4 for the population standard deviation and 42 for the sample mean. Round the final answer to two decimal places.

Margin of error = 1.40

The salaries of top executives at public companies are normally distributed with a population standard deviation of 17 thousand dollars and an unknown population mean. A random sample of 27 executives is taken and results in a sample mean of 319 thousand dollars. Find the margin of error for a 95% confidence interval for the population mean. z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.

Margin of error: 6.41

Adult entrance fees to amusement parks in the United States are normally distributed with a population standard deviation of 2.5 dollars and an unknown population mean. A random sample of 22 entrance fees at different amusement parks is taken and results in a sample mean of 61 dollars. Find the margin of error for a 99% confidence interval for the population mean. z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.

Margin of error:1.37

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. z0.10 = 1.282 z0.05 = 1.645 z0.025 = 1.960 z0.01 = 2.326 z0.005 = 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.

Answer: 210.76

The population standard deviation for the number of pills in a supplement bottle is 16 pills. If we want to be 95% confident that the sample mean is within 5 pills of the true population mean, what is the minimum sample size that should be taken? z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 Use the table above for the z-score, and be sure to round up to the next integer.

Answer: 40 Supplement bottles

Suppose the scores of a standardized test are normally distributed. If the population standard deviation is 3 points, what minimum sample size is needed to be 90% confident that the sample mean is within 2 points of the true population mean? z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 Use the table above for the z-score, and be sure to round up to the next integer.

Answer: 7

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. Once a confidence interval is calculated, the interpretation should clearly state the confidence level (CL), explain what population parameter is being estimated, and state the confidence interval.

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=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 Use the table above for the z-score, and be sure to round up to the nextinteger.

Sample Size 15

In a recent survey, a random sample of 941 biologists were asked about the health of a certain salmon habitat. 361 reported that they thought the salmon habitat was healthy. What value of z should be used to calculate a confidence interval with an 80% confidence level? z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576

Value of z score: 1.282

In a recent questionnaire about food, a random sample of 970 adults were asked about whether they prefer eating fruits or vegetables, and 458 reported that they preferred eating vegetables. What value of z should be used to calculate a confidence interval with a 95% confidence level? z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576

Value of z0.025: 1.960

Suppose weights of running shoes are normally distributed and have a known population standard deviation of 1 ounces and an unknown population mean. A random sample of 24 running shoes is taken and gives a sample mean of 13 ounces. What is the correct interpretation of the 80% confidence interval?

We estimate with 80% confidence that the true population mean is between 12.74 and 13.26 ounces. Once a confidence interval is calculated, the interpretation should clearly state the confidence level (CL), explain what population parameter is being estimated, and state the confidence interval. We estimate with 80% confidence that the true population mean is between 12.74 and 13.26 ounces.

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 = 1.282 z0.05 = 1.645 z0.025 = 1.960 z0.01 = 2.326 z0.005 = 2.576

Z = 1.96

The length, in words, of the essays written for a contest are normally distributed with a population standard deviation of 442 words and an unknown population mean. If a random sample of 24 essays is taken and results in a sample mean of 1330 words, find a 99% confidence interval for the population mean. z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 You may use a calculator or the common z values above. Round the final answer to one decimal places, if necessary.

confidence interval: (1097.6,1562.4)

Suppose scores of a standardized test are normally distributed and have a known population standard deviation of 11 points and an unknown population mean. A random sample of 15 scores is taken and gives a sample mean of 101 points. Find the confidence interval for the population mean with a 98% confidence level. z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 You may use a calculator or the common z values above. Round the final answer to two decimal place

confidence interval: (94.39, 107.61)

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=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 Use the table above for the z-score, and be sure to round up to the next integer.

minimum sample size 73

In a recent survey, a random sample of 1,625 people shopping for a new car were asked whether they would pay the sticker price for the car. 926 reported that they would wait for the salesman to make a better offer on the car before purchasing it. What value of z should be used to calculate a confidence interval with a 90% confidence level? z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576

value of z = 1.645

Suppose weights of running shoes are normally distributed and have a known population standard deviation of 1 ounce and an unknown population mean. A random sample of 24 running shoes is taken and gives a sample mean of 13 ounces. Identify the parameters needed to calculate a confidence interval at the 80% confidence level. Then find the confidence interval. z0.10=1.282 z0.05=1.645 z0.025=1.960 z0.01=2.326 z0.005=2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places, if necessary.

x = ​ 13 σ = ​ 1 n = ​ 24 z α/2​​ = ​ 1.282 (12.74,13.26 )

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. z0.10 = 1.282 z0.05 = 1.645 z0.025 = 1.960 z0.01 = 2.326 z0.005 = 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.

x = ​ 58 σ = ​ 8 n = ​ 25 z α/2​​ = ​ 2.576 (53.88, 62.12)