Question

What is the point estimate for the population mean?

In your own words, what is the margin of error? Why is it so important for constructing a confidence interval?

Suppose that I construct a confidence interval for the mean test grade on exam 1 using Statcrunch and get Upper Limit, 68.9 and a lower limit 76.3. State the conclusion for the confidence interval.

What happens to the confidence interval as we increase the sample size? Explain your reasoning (explanations without reasoning will not be given credit.)

When should we use the t-distribution instead of the z-distribution?

Answer 1

1)

Point estimate is the best estimate for the population mean and is estimated by sample mean.

2)

Margin of error tells us that by how many points our mean will differ by actual population mean.

It is important in the calculation of confidence interval because it helps in making conclusion and gives us the way to conclude that our true population mean would lie in certain interval with certain confidence.

3)

If the confidence interval has a confidence level of 95% then

We are 95% confident that true population mean lies in this interval or in between 68.9 and 76.3

4)

Confidence interval = (Mean - MOE, Mean + MOE)

that is width of the interval depends on margin of error

As the margin of error increases, width increases and vice versa

Now margin or error = z*s.d/√n

That is margin of error is inversely proportional to the sample size

So as the sample size increases, margin of error decreases and hence the width of the confidence interval decrease

5)

When the population s.d is known then we use z

And if population s.d is unknown and we are given with the sample s.d as the best estimate then we use t distribution