A researcher expects that there is a significant difference

A researcher expects that there is a significant difference in pay for public employees in State A compared to State B. Public employees in State A are paid an average of = $12.50 an hour. Just over the border in State B, summary statistics on wages are not available, but a random sample of 4 public employees (This is too small of a sample, but I do not want to make this too time consuming either) are paid the wages below. Make sure to use the appropriate t-test for this analysis!

$8

$8

$16

$8

What is the null and alternative hypothesis (in symbols) for this t-test? (1 point)

What is the critical value for this t-test ( = .05)? (1 point)

Calculate the appropriate t-test statistic (by hand) and determine if it is significant ( = .05) (2 pts)

d. State your conclusion in APA format. (2 points)

Solution

Set Up Hypothesis
Null Hypothesis H0: U=12.5
Alternate Hypothesis H1: U!=12.5
Test Statistic
Population Mean(U)=12.5
Sample X(Mean)=7.5
Standard Deviation(S.D)=1
Number (n)=4
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =7.5-12.5/(1/Sqrt(3))
to =-10
| to | =10
Critical Value
The Value of |t | with n-1 = 3 d.f is 3.182
We got |to| =10 & | t | =3.182
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -10 ) = 0.0021
Hence Value of P0.05 > 0.0021,Here we Reject Ho

We conclude that there is a significant difference in pay for public
employees in State A compared to State B