In 2011 a survey by the American Bar Association indicated t

In 2011 a survey by the American Bar Association indicated that the average yearly income of attorneys was $110,000. A sample of 81 attorneys was taken in 2012 and it reflected an average yearly income of $120,000. Assume the standard deviation of the population of attorneys in 2012 is $36,000.

A) We want to test to determine if there has been a significant increase in the average yearly income of attorneys. Provide the null and alternative hypotheses

B) Compute the test statistic

C) Determine the p-value; and at 95% confidence, test the hypotheses

Solution

Set Up Hypothesis
Null, H0: U=110000
Alternate, H1: U>110000
Test Statistic
Population Mean(U)=110000
Given That X(Mean)=120000
Standard Deviation(S.D)=36000
Number (n)=81
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=120000-110000/(36000/Sqrt(81)
Zo =2.5
| Zo | =2.5
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.5 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 2.5 ) = 0.0062
Hence Value of P0.05 > 0.0062, Here we Reject Ho

ANS:
a) H0: U=110000, H1: U>110000

b)
Zo =2.5

c)
P-Value : Right Tail - Ha : ( P > 2.5 ) = 0.0062
there has been a significant increase in the average yearly income of attorneys