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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.

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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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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

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