Answered: Using R Here we will investigate the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Using R

Here we will investigate the “confidence level” of each of the confidence intervals:
percentile, normal, basic, and BCa. The confidence level of a confidence interval is the longrun proportion that the interval contains the parameter. So, if we took 100 samples and
computed a 95% CI that estimates the population mean mu, the intervals should contain it
95% (95 out of 100) of the time.
1(a). Simulate samples X of size n=10 from an exponential distribution with rate =
1/50. Run a bootstrap procedure to estimate the median. Compute the 4 CI’s mentioned
above. Repeat this 1,000 times and estimate the confidence level of each type of confidence
interval.
1(b). Are the confidence intervals below or above the confidence level of .95? Why
do you think this is? Explain.
1(c). Repeat this for samples of size n=50.
1(d). Did the confidence level of the intervals change with the sample size? Are the
confidence intervals below or above the confidence level of .95? Why do you think this is?
Explain.
remember: you can put ‘warning=FALSE’ in the R chunk to not print warnings

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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