Question

Consider H₀: μ = 31 versus H₁: μ ≠ 31. A random sample of 36 observations taken from this population produced a sample mean of 28.84. The population is normally distributed with σ = 6.

(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

a)

= / sqrt(n)

= 6 / sqrt(36)

= 1

b)

Test statistics

z = - /

= 28.84 - 31 / 1

= -2.16

c)

P( Z < z) = P( Z < -2.16) = 0.0154

d)

p-value = 2 * P( Z < z)

= 2 * P( Z < -2.16)

= 2 * 0.0154

= 0.0308