Archeology Archeologists have studied sizes of Egyptian skulls...

Question

Archeology Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures. Listed below are the widths (mm) of skulls from 150 A.D. (based on data from Ancient Races of the Thebaid by Thomson and Randall-Maciver).

a. Use 1000 bootstrap samples to construct a 99% confidence interval estimate of the mean skull width.

a. Use 1000 bootstrap samples to construct a 99% confidence interval estimate of the mean skull width.

Accepted Answer

Hello 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. Scientists are studying the sizes of pottery shards found in ancient Roman settlements to determine if there was a shift in pottery styles over time. Below are the diameter values in units of millimeters of pottery shards from the year 200 AD. Pottery shard diameters are curly brackets of 125, 140, 133, 150, 160, 155, 145, 132, 138, 148. Using 10 bootstrap samples, construct a 99% confidence interval estimate of the mean pottery shard diameter. The 10 bootstrap sample means are 137.6, 139.1, 139.1, 139.2, 139.3, 139.3, 139.6, 139.6, 139.6, 139.6. Awesome. So it appears for this particular prong we're ultimately asked to take our 10 bootstrap samples that are given to us by the prom itself, and we're asked to construct or create a 99% confidence interval to help us estimate the mean pottery shard diameter. So that's our final answer we're ultimately trying to solve for. So with that in mind, our first step that we need to take to solve this problem is we need to go ahead and note that the bootstrap mean values are already in ascending order, because we're told that 137.6 is our lowest number and our highest number is 139.6, and as you can see, it's already written in ascending order in the prom itself. And, and we need to note once again that for a 99% confidence interval, we need to trim 0.5% in each tail, so therefore we need to use the 0.5 0.5s. And 99.5 it's percentiles of these 10 values. So we need to note that the 99.5. Percentile corresponds to the 10th value, which is going to be equal to 139.6 millimeters. Awesome. And we also need to note that the 0.5 percentile corresponds to the first value, which is equal to 137.6 millimeters. So that will mean therefore, as a result, the 99% confidence interval will have to be 137.6 millimeters. Which is our unit of measurement, is going to be less than And we're gonna use the we're gonna use the Greek letter mu to denote mean. So 137.6 millimeters is less than mu, where mu is our mean and mu is less than 139.6 millimeters. And that's it. That is our final answer. Hooray, we did it. So once again, without a doubt, our final answer has to be 137.6 millimeters is less than mu and mu is less than 139.6 millimeters. 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 Calculation

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