Mean Body Temperature Data Set 5 “Body Temperatures” in Append...

Question

Mean Body Temperature Data Set 5 “Body Temperatures” in Appendix B includes 106 body temperatures of adults for Day 2 at 12 AM, and they vary from a low of 96.5F to a high of 99.6F. Find the minimum sample size required to estimate the mean body temperature of all adults. Assume that we want 98% confidence that the sample mean is within 0.1F of the population mean.

b. Assume that sigma=0.62F, based on the value of s=0.62F for the sample of 106 body temperatures.

b. Assume that sigma=0.62F, based on the value of s=0.62F for the sample of 106 body temperatures.

Accepted Answer

Below there. Today we're going 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 nutritionist wants to estimate the mean daily calcium intake for teenagers. She wants to be 99% confident. That the sample mean is within 20 mg of the true meat. If the population standard deviation is known to be 85 mg, what is the minimum sample size that is required? Awesome. So it appears for this particular prompt we're asked to determine what the minimum sample size that is required in order for the population standard deviation to be 85 mg considering all the other information that's provided to us by the prom itself. So we are told that the sample mean is within 20 mg of the. True mean, and we're also told that she wants 99% confidence that the sample mean is within 20 mg of the true mean. And we're told that if the population standard deviation is known to be 85 mg, we're asked to determine ultimately what is the minimum sample size that is required. So that is our final answer we're ultimately trying to solve for. What is the sample size? So with that said, let's read off our multiple choice answers to see what our final answer might be. So A is 80, B is 90, C is 110, and D is 120. Awesome. So, first off, in order to find the minimum sample size, we need to recall and use the following formula, which states that N is equal to parentheses Z multiplied by sigma divided by E all to the power of 2. So, with that said, let us quickly note that when we write down all of our known variables, these are the variables that are given to us. Let us note that we're told that the confidence level is 99%, so that will mean that our value for Z is going to be equal to 2.576, and we should be able to find this Z score value from our table that's located in your textbook. And we're told that the standard deviation is, that's what Sigma represents. Sigma, our standard deviation, is equal to 85 mg. And we're told that our margin of error, which will denote as E in the margin of error, is given to us as 20 mg. Fantastic. So now all we need to do to solve for our final answer is we need to plug in all of our known variables into our expression and solve for N. And when we do that, we will find that N is equal to parentheses 2.576 multiplied by. 85. Milligrams, divided by 20. Milligrams. All to the power 2, which when we plug that into our calculator, we will find that it is approximately equal to 119.86, which when we round this to the nearest whole number, we will find that N is approximately equal to 120, and that is our final answer. Hooray, we did it. So to quickly recap what we've learned, as we should note, therefore, the minimum sample size required is 120. In order to estimate the mean daily calcium intake for teenagers with a 99% confidence and a margin of error of 20 mg, so that will mean our final answer without a doubt has to be multiple choice answer letter D, which once again is 120. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Sample Size Determination

Confidence Interval

Standard Deviation and Population Variance

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