Question

18. The income of a group of financial brokers is normally distributed. A sample of 14 of the brokers has an average yearly income of $86,000. Suppose the population standard deviation is $12,000. Test with α = 0.05 whether the yearly mean income of the group of brokers is more than $80,000.

a. State and label the null and alternative hypotheses. (2 points)

b. State the value of the test statistic. (2 points)

c. Find either the critical value(s) and draw a picture of the critical region(s) or find the P-value for this test. Indicate which method you are using: ( CIRCLE ONE: Critical value / P -value ) (3 points)

d. State your conclusion in the context of this problem, citing the reason from your selected method. (3 points)

Answer 1

a)

Null Hypothesis, 80000

Alternative Hypothesis, 80000

b)

test statistic,

z = (86000 - 80000)/(12000/sqrt(14))
z = 1.87

c)

This is right tailed test,
P-value = P(z > 1.87) = 0.0307

Here the significance level, 0.05. This is right tailed test; hence rejection region lies to the right. 1.645 i.e. P(z > 1.645) = 0.05

d)

As p-value < 0.05, reject H0
There is sufficient evidence to conclude that the yearly mean income of the group of brokers is more than $80,000.