Sample Size for Mean Find the sample size required to estimate...

Question

Sample Size for Mean Find the sample size required to estimate the mean IQ of airline pilots. Assume that we want 99% confidence that the mean from the sample is within two IQ points of the true population mean. Also assume that sigma=15

Accepted Answer

Hello there. Today we're to solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A transport researcher wants to estimate the average one-way commute time in units of minutes for city workers. How large a sample is needed such that with 99% confidence, the sample mean is within. 3 minutes of the true population mean. Assume that the population standard deviation is sigma is equal to 12 minutes. Awesome. So it appears for this particular problem, we're trying to determine how large of a sample is required or needed such that with 99% confidence, the sample mean will lie within 3 minutes of the true population mean, and we're also asked to assume that the population standard deviation is going to be equal to 12 minutes. So with that in mind, Our first step is we need to identify the critical value. So, let us note that for the confidence level, which I'll call CL for short, so the confidence level of 99%. So for a confidence level of 99%, we need to note that The subscript. Alpha divided by 2 is going to be equal to Z subscript 0.005, which is gonna be approximately equal to 2.576, where this Z represents the Z score. Awesome. So once again, Z subscript 0.005 is approximately equal to 2.576. Our second step is we need to set the desired margin of error, so we need to note that the margin of error that we want, which we'll call E, is going to be equal to 3 minutes, and our third and final step. we need to use the sample size formula for a mean or sigma is known, so we need to recall and use the sample size formula. So we need to recall that N is equal to Z, multiplied by alpha divided by 2, multiplied by sigma, all divided by E and this expression is going to be all to the power of 2. So when we plug in our known variables, we will find that N is equal to parentheses 2.576 multiplied by 12, all divided by 3, all to the power of 2, which will be approximately equal to 106. 0.15 which when we round to the nearest whole number because we can't have part of a person, we will find that our rounded answer will be 107. So that means that N equals 107, and that is our final answer. Hooray, we did it. So therefore, without a doubt, our final answer has to be 107, so 107 city workers, and that's it. We've officially solved for this problem. Hooray, we did it. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. I.

Sample Size for Mean Find the sample size required to estimate the mean IQ of airline pilots. Assume that we want 99% confidence that the mean from the sample is within two IQ points of the true population mean. Also assume that sigma=15

Key Concepts

Sample Size Calculation

Confidence Level

Margin of Error

Watch next