Question

The Department of Labor would like to test the hypothesis that the average hourly wage for recent college graduates is less than $20. A random sample of 24 recent college graduates averaged $19.30 per hour with a standard deviation of $3.20 per hour. The Department of Labor would like to set ? = 0.10. Use the critical value approach to test this hypothesis.

Answer 1

Answer:

The claim is false that t the average hourly wage for recent college graduates is less than $20.

Step-by-step explanation:

Claim : The Department of Labor would like to test the hypothesis that the average hourly wage for recent college graduates is less than $20.

n = 24

Since n < 30

So, we will use t test

x = 19.30

$\mu = 20$

s = 3.20

$H_0:\mu\geq 20\\H_a:\mu <20$

Formula : $t =\frac{x-\mu}{\frac{s}{\sqrt{n}}}$

Substitute the values :

$t =\frac{19.30-20}{\frac{3.20}{\sqrt{24}}}$

$t =-1.071$

Degree of freedom = n-1 = 24-1 = 23

 α=0.10

So, using t table  

$t_({\frac{\alpha}{2},d.f.}) = 1.714$

t critical > t calculated

So we accept the null hypothesis

So, The claim is false that t the average hourly wage for recent college graduates is less than $20.