Question

A random sample of n=100 observations produced a mean of x̅=33 with a standard deviation of s=5.

(a) Find a 95% confidence interval for μ Lower-bound: Upper-bound:

(b) Find a 99% confidence interval for μ Lower-bound: Upper-bound:

Answer 1

a)

t critical value at 0.05 level with 99 df = 1.984

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

33 - 1.984 * 5 / sqrt(100) < < 33 + 1.984 * 5 / sqrt(100)

32.008 < < 33.992

Lower bound = 32.008

Upper bound = 33.992

b)

t critical value at 0.01 level with 99 df = 2.626

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

33 - 2.626 * 5 / sqrt(100) < < 33 + 2.626 * 5 / sqrt(100)

31.687 < < 34.313

Lower bound = 31.687

Upper bound = 34.313