Determine the sample size needed to obtain an estimate of mu if the margin of error E=0.10,sigma =0.75, and the confidence level is 998 (use z_(0005)=2.57 ).
Use Table IV in Appendix C to compute the probabilities.
Recall the following definitions from section 8.8 of the text.
Given the confidence level and the standard deviation of the population, the sample size that will produce a predetermined margin of error E of the confidence interval estimate of mu is n=(z^(2)sigma ^(2))/(E^(2))
where the value of z is obtained from the standard normal distribution (Table IV in Appendix C or by calculator) and the quantity zsigma _(x) is called the Margin of Error and is denoted by E. Furthermore, sigma _(ar{x} )=(sigma )/(sqrt(n)) is the standard deviation of ar{x} .
Alternatively, To obtain z from a graphing calculator, we use the formula z= invNorm (1-(alpha )/(2),mu ,sigma )
where mu is the mean and sigma is the standard deviation of the normal distribution. For the standard normal distribution mu =0 and sigma =1. Recall that in general z= invNorm("area to left of z,mu,sigma.
Chapter 08, Section 8.2, Intelligent Tutoring Problem 017
It is given that E=0.10 and sigma =0.75.
(a) Find a for 99% confidence level.
(b) Find 1-(a)/(2)
1-(a)/(2)=â—»
(c) Find z_((a)/(2)) for 399% confidence level.
z_((0)/(2))
use z0.005=2.57
Use Table IV in AppendixC to compute the probabilities
Recall the following definitions from section 8 of the text Given the confidence level and the standard deviation of the population,the sample size that will produce a predetermined margin of errorEof theconfidence intervalestimate ofisn= 2202 E2 where thevalue of z is obtained from the standard normal distribution(Table IVin Appendix Cor by calculator)and the quantity zo is called the Margin of Error and is denoted by E.Furthermore, V is the standard deviation of x
Alternatively.To obtain z from a graphing calculator.we use the formulaz=invNorm(1-a/2.g where is the mean and g is the standard deviation of the normal distribution.For the standard normal distribution=O and a=1 Recall that in generalz=invNormarea to left of z
Chapter08.Section 8.2,Intelligent Tutoring Problem017
It is given thatE=0.10anda=0.75
(aFind a for99%confidence level
(bFind1-a/2
1-a/2=
(c)Find za/for a99%confidence level
Za/2
