Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar​, is found to be 110​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct a 96​% confidence interval about mu if the sample​ size, n, is 16. ​(b) Construct a 96​% confidence interval about mu if the sample​ size, n, is 27. ​(c) Construct a 99​% confidence interval about mu if the sample​ size, n, is 16. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

Answer 1

We don't know the population standard deviation. So, we have to use t-distrbution. But we have the estimates as

a)

b)

For n =27, 96% CI

c)

99% CI for n =16

d)

No, we could not have computed if the population is not normally distributed. Because all the sample sizes are less than 30, so we can not approximate the distribution to be normal