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

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

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 =(x-\mu)/((s)/(√(n)))`

Substitute the values :

`t =(19.30-20)/((3.20)/(√(24)))`

`t =-1.071`

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

α=0.10

So, using t table

`t_({(\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.