A sample of the math test scores of 35 fourth-graders has a mean of 82 with a standard deviation of 15.
Find the 95% confidence interval of the mean math test cores of all fourth-graders.
Find the 99% confidence interval of th mean math test scores of all fourth-graders
Which interval is larger? Why

A researcher is interested in estimating the average salary of fire fighters in a large city. He wants to be 95% confident that his estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within %200

A researcher is interested in estimating the average salary of fire fighters in a large city. he wants to be 95% confident that his estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within %200




Just plug them into the formula. First, what z-score corresponds to 95% C.I.?.

It is z=1.96

Now, use the formula:

n=\left(\frac{z\cdot {\sigma}}{E}\right)^{2}

Plug in your given values and you have it.

A sample of the math test scores of 35 fourth-graders has a mean of 82 with a standard deviation of 15.
find the 95% confidence interval of the mean math test cores of all fourth-graders.
find the 99% confidence interval of th mean math test scores of all fourth-graders
which interval is larger? why

These are very straight forward. Nothing fancy.

E=z\cdot\frac{\sigma}{\sqrt{n}}

Find that value using your data, then add it to and subtract it from the mean.

You do not have a sample size. Did you forget it?

If they did not give you a sample size, assume one and see what happens to the confidence interval as you change from .90 to .95 to .99.

Does it widen? Narrow?