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 106 ​, and the sample standard​ deviation, s, is found to be 10 . ​(a) Construct an 95 ​% confidence interval about mu if the sample​ size, n, is 18 . The Lower Bound and Upper Bound ​(b) Construct an 95 ​% confidence interval about mu if the sample​ size, n, is 25 . The Lower Bound and Upper Bound How does decreasing the sample size affect the margin of​ error, E? A. As the sample size decreases ​,the margin of error stays the same. B. As the sample size decreases, the margin of error increases. C. As the sample size decreases ,the margin of error decreases. ​(c) Construct a 96 ​% confidence interval about mu if the sample​ size, n, is 18. ​The Lower and Upper Bound (d) Could we have computed the confidence intervals in parts​(a)-(c) if the population had not been normally​ distributed?

Answer 1

Solution:-

(a) for n = 18
95% Confidence interval about mu = (101.027,110.973)

(b) for n = 25
95% Confidence interval about mu = (101.872,110.128)

(c) option B. As the sample size decreases, the margin of error increases.

(d) No, the population needs to be normally distributed.