Question

In: Statistics and Probability

What are the confidence intervals for a population mean? Provide examples.

Question 2

Question 3

A confidence interval for the population mean when the population follows the normal distribution and the population standard deviation is known is computed by? Provide examples.

Solutions

Expert Solution

Question 2:

When standard deviation is unknown:

The confidence interval for mean is:

Here shows the sample mean and s shows the standard deviation. The statistics n shows the sample size. And t shows the critical value of t.

Example:

Here we have

Since there 16 data values in the sample so degree of freedom is df=16-1=15 and critical value of t for 95% confidence interval, using excel function "=TINV(0.05,15)" is 2.131.

The required confidence interval is

Therefore, a 95% confidence interval for the mean is (24.19, 27.81).

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When standard deviation is known:

The confidence interval for mean is:

Here shows the sample mean and shows the populaition standard deviation. The statistics n shows the sample size. And z shows the critical value of z.

Example:

Given information:

For 85% confidence interval, using excel function "=NORMSINV(0.925)", critical value of z is . So required confidence interval is

Therefore, a 85% confidence interval for the mean is (23.4, 24.6).

orchestra answered 1 year ago

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