Analysis of Last Digits Weights of respondents were recorded a...

Question

Analysis of Last Digits Weights of respondents were recorded as part of the California Health Interview Survey. The last digits of weights from 50 randomly selected respondents are listed below.

Last digits of weights from 50 respondents: 5, 0, 1, 0, 2, 0, 5, 0, 5, 0, 3, 8, 5, 0, 5, 5, 6, 0, 0, 0, 0, 8, 5, 5, 0, 4, 5, 0, 4, 0, 0, 0, 0, 8, 0, 9, 5, 3, 0, 5, 0, 0, 5, 8.

a. Use the bootstrap method with 1000 bootstrap samples to find a 95% confidence interval estimate of .

Accepted Answer

Below there today we want 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 pediatrician measures head circumference in centimeters of 12 healthy newborns and finds a Sample standard deviation of S equals 0.49 centimeters. To gauge the precision of this estimate, she takes 10 bootstrap samples with replacement of size 12 and computes each sample standard deviation. The sorted bootstrap standard deviations in centimeters are. 0.45 0.48 0.49 0.50 0.51 0.52 0.54, 0.56 0.58. 0.60. Using these 10 values, construct a 95% bootstrap confidence interval for the true population standard deviation sigma. Awesome. So it appears for this particular prom, we're asked to take our 10 values that are provided to us by the prom itself, and we're asked to construct a 95% bootstrap confidence interval, CI for short, for the true population standard deviation sigma. So with that said, our first step is we need to recall and note that for a 95% confidence interval, The drop or drop, we need to drop the lowest 2.5% and the highest 2.5% of the sorted bootstrap standard deviations. So since we're only given 10 values that correspond approximately to taking the first and 10th values as the lower and upper bounds since we're only given these 10 values. So, when we check these given bootstrap standard deviations, we'll see when we look at our 10 values that are provided to us, they are already assorted in ascending order, meaning from lowest to highest. So that means 0.45, 0.48, 0.49, 0.50, 0.51. 0.52, 0.54, 0.56, 0.58, and 0.60. is in numerical order. So, therefore, without a doubt, our lower bound, which I'll call LB for short, our lower bound is going to be equal to 0.45 centimeters, and let us know that this is our first value. Fantastic. So once again, that's our first value, and our upper bound, which I'll call UB and our upper bound is equal to 0.60 centimeters. And this is our 10th value. So that will mean ultimately, that the 95% bootstrap confidence interval for sigma will be 0.45 centimeters is less than sigma, and sigma is less than 0.60 centimeters. So that will mean, without a doubt that our final answer has to be, once again, 0.45 centimeters is less than sigma and sigma is less than 0.60 centimeters. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Analysis of Last Digits Weights of respondents were recorded as part of the California Health Interview Survey. The last digits of weights from 50 randomly selected respondents are listed below.

a. Use the bootstrap method with 1000 bootstrap samples to find a 95% confidence interval estimate of .

Key Concepts

Bootstrap Method

Confidence Interval

Sampling Distribution

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