Question

simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar​, is found to be 112​, and the sample standard​ deviation, s, is found to be 10.

​(a) Construct a 90​% confidence interval about mu if the sample​ size, n, is 19. ​

(b) Construct a 90​% confidence interval about mu if the sample​ size, n, is 12. ​

(c) Construct an 80​% confidence interval about mu if the sample​ size, n, is 19. ​

(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

Answer 1

a. Here n=19<30, but distribution is normal we will use t distribution

t table value for 90% CI is TINV(0.1,18)=1.734

So Margin of Error is

So CI is

b. Here n=12<30, but distribution is normal we will use t distribution.

t table value for 90% CI is TINV(0.1,11)=1.796

So Margin of Error is

So CI is

c. Here n=19<30, but distribution is normal we will use t distribution

t table value for 80% CI is TINV(0.2,18)=1.330

So Margin of Error is

So CI is

d. If distribution is not normal, we wont be able to find CI