Freshman 15 Here is a sample of amounts of weight change (kg) ...

Question

Freshman 15 Here is a sample of amounts of weight change (kg) of college students in their freshman year (from Data Set 13 “Freshman 15” in Appendix B): 11, 3, 0, , where represents a loss of 2 kg and positive values represent weight gained. Here are ten bootstrap samples:
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a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population.

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a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population.

Accepted Answer

Hello there. Today we're gonna 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 sports psychologist measures the change in reaction time in units of seconds for 12 athletes before and after a specialized training program. Negative values indicate a faster reaction time post training. The observed sample is curly brackets of -0.4 0.1 0.2, 0.3. 0.0 0.1, 0.5, 0.3, 0.2, 0.4 0.5, 0.6. 10 bootstrap samples with the replacement of size 12 are drawn, and their means in ascending order turn out to be. 0.47, 0.32, 0.18 0.05. 0.08, 0.17, 0.29 0.41, 0.52, 0.67. Using only these 10 bootstrap means construct an 80% confidence interval estimate for the true mean change in reaction time. Awesome. So it appears for this particular prompt, we're asked to use only these 10 bootstrap means to create or construct an 80% confidence interval, which is denoted as CI. So we're trying to create an 80% confidence interval to estimate for the true mean change in reaction time, and that is our final answer that we're ultimately trying to solve for. So, with that said, our first step that we need to take is we need to note and recall that the bootstrap means are already in ascending order. So we're told that it's like as we're told in the problem itself, -0.47, 0.32, 0.18, 0.05, 0.08, 0.17, 0.29, 0.41, 0.52, and 0.67. And for an 80% confidence interval, so let's make a note of this, once again, so we're trying to figure out an 80% confidence interval CI for short. We need to note that alpha, in this case is going to be equal to 0.20. Antaip is 80 + 20 equals 100. And a like a 20% as a decimal is 0.20. So that will mean as a result that alpha divided by 2 is going to be simply equal to 0.10, so 10%. And we need to also note that N, in this case is going to be equal to 10, and K will be equal to alpha divided by 2, multiplied by N which is going to be equal to 0.10, multiplied by 10, which is going to be simply equal to 1. Fantastic. So therefore, as a result, we will trim the lowest and highest values. So our lower bound, which we'll call LB for short, our lower bound will be equal to -0.32, and we need to note that this will be our second value in our data set. And our upper bound, which we'll call UB, our upper bound will be equal to 0.52, and let us know that this will be our ninth value in our data set. Fantastic. So therefore, the 80% confidence interval will be negative 0.32 seconds is less than mu, where mu denotes the mean and mu will be less than 0.52 seconds, and that is our final answer. Hooray, we did it. So to quickly recap once again, our final answer without a doubt has to be -0.32 seconds is less than mu, and mu is less than 0.52 seconds. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Bootstrap Sampling

Confidence Interval

Mean Weight Change

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