Student ID: Page 5 of 6 Problem#3(8 pts) Consider a normal population distributi
ID: 3349840 • Letter: S
Question
Student ID: Page 5 of 6 Problem#3(8 pts) Consider a normal population distribution with an unknown and known standard deviation =3 A confidence interval for is given by the following formula. Vn 1.9 1-what is the confidence level (CD for the interval- 2-Compute a 98% confidence interval for when n = 49 and = 80 3-How much is the error associated with the 98% confidence interval for found in question 2? 4, Find the sample size, n, for which the 98% confidence interval for has a maximum error of 0.7Explanation / Answer
Solution1:
Z crit for 95%=1.96
So the given interval is 95% confidence interval for the mean.
Solution2:
Z crit for 98% =2.33
sigma=3
mean=80
n=49
98% confidence interval for mean is
80-2.33(3/sqrt(49),80+2.33(3/sqrt(49)
79.00143,80.99857
lower limit=79.00143
upper limit=80.99857
Solution3:
margin of error
=Z crit(sigma)/sqrt(n)
=2.33(3/sqrt(49)
=0.9985714
Solution4:
maximum error=0.7
n=(Z sigma/m)^2
=(2.33*3/0.7)^2
=99.71449
=100
sample size=n=100
Required sample size=n=100