Confidence Intervals

Question 1 

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately sigma = 28.6. You would like to be 98% confident that your estimate is within 3 of the true population mean. How large of a sample size is required? Do not round mid-calculation.

Question 2

You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately sigma = 54.6 dollars. You would like to be 99% confident that your estimate is within 4 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?

Question 3

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately sigma = 29.8. You would like to be 95% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?

Question 4

You measure 26 turtles' weights, and find they have a mean weight of 34 ounces. Assume the population standard deviation is 6.9 ounces. Based on this, what is the maximal margin of error associated with a 99% confidence interval for the true population mean turtle weight. 

Give your answer as a decimal, to two places 

Question 5

An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 2.2 mm, how many of these components should she consider to be 99% sure of knowing the mean will be within ± 0.5mm?

22

129

105

622

12

Question 6

An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 1.1 mm, how many of these components should she consider to be 80% sure of knowing the mean will be within ± 0.4mm? 

16

13

4

6

11

Question 7

A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only wants a 8% margin of error at a 99% confidence level, what size of sample is needed? Give your answer in whole people. 

Question 8

Based on historical data in Oxnard college, we believe that 30% of freshmen do not visit their counselors regularly. For this year, you would like to obtain a new sample to estimate the proportiton of freshmen who do not visit their counselors regularly. You would like to be 95% confident that your estimate is within 1.5% of the true population proportion. How large of a sample size is required? Do not round mid-calculation.

Question 9

A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only wants a 2% margin of error at a 99% confidence level, what size of sample is needed? When finding the z-value, round it to four decimal places.

Question 10

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 59%. You would like to be 90% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required?

Question 11 

A pollster wishes to estimate, with 95% confidence, the proportion of people who believe that recent changes in climate are primarily due to human activity. 

Find the minimum sample size necessary to achieve a margin of error of less than 1%.

a. Assuming no previous estimates are available. Round your answer up to the next integer.

b. Assuming a previous estimate of 0.25. Round your answer up to the next integer.

Question 12

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 79%. You would like to be 90% confident that your estimate is within 1.5% of the true population proportion. How large of a sample size is required? Do not round mid-calculation.