Question

Confidence intervals are a way to make predictions about entire populations using a random sample. Suppose you do not know the value for a certain population mean, such as the average miles per gallon for some new brand of car. You don’t have the data for every single car of this new brand, so you can’t calculate the population mean. However, you can try to estimate it. What value is the point estimate for the population mean? Describe, in your own words, what the point estimate represents. •Suppose you would like to construct a 90 percent confidence interval. What would be the margin of error for this interval? •What would be the lower and upper limits for this 90 percent confidence interval? •Now that you have constructed the interval, define its meaning in your own words

Answer 1

Sample mean is the point estimate for the population mean. Because it is the best guess for the population mean.

what the sample I have, I shall find sample standard deviation

$Let \ sample \ mean= \overline{x}, standard \ dev = s$

and the sample size is 'n'

$Margin \ of\ error\ (E)= t_{0.05,n-1} \frac{s}{\sqrt{n}}$

$Lower - Bound =\overline{x}-E$

$Upper - Bound =\overline{x}+E$

We are 90% confident on the basis of sample data the population mean will fall within this range(lower to upper bound)