Question

2. A random sample of 100 graduates of a certain secretarial school typed an average of 90 words per minute with a sample standard deviation (s) of 10 words per minute. We assume a normal distribution for the number of words typed per minute. (a) (4pts) Find a 95% confidence interval for the average number of words t yped per minute of all graduates of this school. (b) (3pts) Suppose the population standard deviation (o) is exactly 10 words per minute. How large a sample size is needed if we wish to be 95% confident that our sample mean will be within 2 words of the true mean for the average number of words typed per minute?

Answer 1

a)

95% confidence interval is

$\bar{x}$ - t * S / sqrt(n) < $\mu$ < $\bar{x}$ + t * S / sqrt(n)

90 - 1.984 * 10 / sqrt(100) < $\mu$ < 90 + 1.984 * 10 / sqrt(100)

88.016 < $\mu$ < 91.984

95% CI is ( 88.016 , 91.984)

b)

Sample size = ( Z * $\sigma$ / E)²

= ( 1.96 * 10 / 2)²

= 96.04

Sample size = 97 (Rounded up to nearest integer)