Confidence Intervals of 100 Samples 0.5 0.0 0.5 1.0 0.95 1. The red lines show t

Question

Confidence Intervals of 100 Samples 0.5 0.0 0.5 1.0 0.95 1. The red lines show the confidence intervals which do not contain the actual population mean. How does the number of these misses change as you adjust the confidence level? Can you see a connection between the confidence level and the expected number of errors? 2. How does changing the sample size effect the number of errors made (misses)? 3. How does the width (length) of the intervals change as the sample size increases? 4. How does the width(length) of the confidence intervals change as the confidence level increases?

Explanation / Answer

A confidence level of the true mean is given by

mu = x +- Z*s/sqrt(n)

Where x is the sample mean

Z is the value corresponding to the CI

Z values for 90, 95 and 99 CI for a two-tailed test are 1.65, 1.96 and 2.33 respectively

s is the sample standard deviation

n is the sample size

Now let's understand what is a 95% CI

It means that if samples are taken randomly, there is a 95% chance that the samples contain the true mean, mu

Let us now answer the questions-

1) As we increase the CI level, the number of errors come down

There is an inverse relationship between CI level and number of errors

2) n impacts the number of errors

As n increases, CI becomes narrow and chance is that the number of errors go up and vice-versa

3) As n increases, CI becomes narrow

4) The width of the CI is directly proportional to the confidence level

As the CI level increases, the width increases

95% CI is (-10, 300)

It means that there is a 95% probability that the average daily profit falls in the range of the CI obtained

Let me know if you need anything else, if not please don't forget to like the answer :)

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