Question 281474
a sample of the reading scores of 29 fifth gtaders has a mean of x(with the bar on top of the x)=83 and a population standard deviation of r=10.5. 

a. Find 99% confidence interval for the population mean scores of all fifth graders on this test.
---
xbar = 83 ; s = 10.5, so s-hat = 10.5/sqrt(29) = 1.9498
invT(0.995,with df=28) = 2.7633
So, standard error for the population means = 2.7633*
---
95% CI: 83-2.7633 < u < 83+2.7633
95% CI: 80.2367 < u < 85.7633
=========================================
 
b. How big should the sample size be for the margin of error to be no larger that 3.5? 
n = [1.96*10.5/3.5]^2 = 34.57
Rounding up: n = 35
==============================
c. 99% confidence interval if the sample was 29 fifth graders and you were given the sample standard deviation s=10.5 instead of the population standard deviation?