Question

Say we have the following hypotheses

H0: μ <50

HA: μ > 50

We know that the population standard deviation is 8. If we collect a sample of 64 observations and want α = 0.05, calculate whether or not we reject the null for the following sample means: a.x̅=52.5

b.x̅=51

c.x̅=51.8

Answer 1

Solution:

H0: μ <50

HA: μ > 50

> sign in HA indicates "Right tailed test"

= 8

n = 64

α = 0.05

a) x̅ = 52.5

Test statistic

z = (x̅ - μ)/(/n) = ((52.5 - 50)/(8/64) = 2.50

p value = P(Z > 2.50) = P(Z < -2.50) = 0.0062

Since p value <  α = 0.05

We reject the null hypothesis.

b)  x̅ = 51

Test statistic

z = (x̅ - μ)/(/n) = ((51 - 50)/(8/64) = 1.00

p value = P(Z > 1.00) = P(Z < -1.00) = 0.1587

Since p value > α = 0.05

We do not reject the null hypothesis.

c) x̅ = 51.8

Test statistic

z = (x̅ - μ)/(/n) = ((51.8 - 50)/(8/64) = 1.80

p value = P(Z > 1.80) = P(Z < -1.80) = 0.0359

Since p value < α = 0.05

We reject the null hypothesis.