The height, x cm, of each man in a random sample of 200 men living in the UK was measured. The following results were obtained: 35 050, ' - 6 163 109.

(a) Calculate unbiased estimates of the mean and variance of the heights of men living in the UK.

(b) Determine an approximate 90% confidence interval for the mean height of men living in the UK. Name the theorem that you have assumed. (NEAB)

Example 9.25

(a) Consider T following a t-distribution with 11 degrees of freedom, i.e. v 11 and T-1(11). Find (i) P(T <1.796) (ii) P(T>3.106) (iii) P(|T| <2.201)

Example 9.25

(b) The random variable T has a t-distribution with 14 degrees of freedom, i.e. T-t(14). Find the value of t for which (i) P(T