A random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. Find the 90% confidence interval of the true mean. If a day care center were starting up and wanted to keep tuition low, what would be a resasonable amount to charge?

Question

A random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630.  Find the 90% confidence interval of the true mean.  If a day care center were starting up and wanted to keep tuition low, what would be a resasonable amount to charge?

anonymous · Answer

{3987 - 1.645(630/sqrt(50)), 3987 + 1.645(630/sqrt(50))}

anonymous · Answer

(1.645 is the z value for a 90% confidence interval, because P(z<1.645) = 0.95

anonymous · Answer

So there is 5% above, and 5% below the confidence interval

anonymous · Answer

Thank you!

anonymous · Answer

Sure :-)

anonymous · Answer

Wait, what is the confidence interval of the true mean? is it 5 then? Also, what would be a resonable amount to charge to keep tuition low?

anonymous · Answer

That is the confidence interval for the true mean, it is the range specified above (I would calculate it, but there is no calculator handy). To keep tuition low, choose the lower bound of the interval

anonymous · Answer

3987 - 1.645(630/sqrt(50)), 3987 + 1.645(630/sqrt(50))}? I should calculate this? A bit confused