Question

Consider H0: μ = 29 versus H1: μ ≠ 29. A random sample of 25 observations taken from this population produced a sample mean of 25.42. The population is normally distributed with σ = 8.

(a) Compute σx¯. Round the answer to four decimal places.
(b) Compute z value. Round the answer to two decimal places.

(c) Find area to the left of z–value on the standard normal distribution. Round the answer to four decimal places.

(d) Find p-value. Round the answer to four decimal places.

Answer 1

Given that, population standard deviation (σ) = 8

sample size (n) = 25 and sample mean = 25.42

The null and alternative hypotheses are,

H0: μ = 29 versus H1: μ ≠ 29

a)

b) Test statistic is,

=> Z = -2.24

c) P(Z < -2.24) = 0.0125

Therefore, the area to the left of z-value on the standard normal distribution is 0.0125

d) p-value = 2 * P(Z < -2.24) = 2 * 0.0125 = 0.0250

=> p-value = 0.0250