Question

According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in 1997 were $424.20. Suppose a labor researcher wants to test to determine whether this figure is still accurate today. The researcher randomly selects 54 production workers from across the United States and obtains a representative earnings statement for one week from each. The resulting sample average is $432.69. Assuming a population standard deviation of $33.90, and a 5% level of significance,

1. Develop hypothesis for this research
2. Calculate the test statistic
3. Find the critical value
4. Test the hypothesis using 5% level of significance

Answer 1

(a)

H0: $\mu$ = 424.20

H1: $\mu \neq$ 424.20

(b)

This is z-test as we know the population standard deviation.

test statistic,

$z_0 = \frac{\bar x - \mu}{\sigma} = \frac{432.69 - 424.20}{33.90} = 0.25$

(c)

For 5% level of significance and two tailed test, $z_{\alpha/2}$ = 1.96. So the critical values are -1.96 and +1.96.

(d)

As, |z₀| < 1.96, we fail to reject the null hypothesis and conclude that the average weekly earnings of a production worker is 424.20.

** If the answers do not match please comment.

Answer 2

Is this the right answer