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.
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
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