A simple random sample of sizen is drawn from a population that is normally distributed. The sample

Question:

A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, x, is found to be 108, and the sample standard deviation,s, is found to be 10.

(a) Construct a 96% conﬁdence interval for m if the sample size, n, is 25.

(b) Construct a 96% conﬁdence interval for m if the sample size, n, is 10. How does decreasing the sample size affect the margin of error,E?

(c) Construct a 90% conﬁdence interval for m if the sample size, n, is 25. Compare the results to those obtained in part (a). How does decreasing the level of conﬁdence affect the size of the margin of error,E?

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