Question

Suppose researchers have reported that the population mean for the annual salary of certified welders was $40,000, and the population standard deviation was $5200. A new survey of 200 welders was taken, and the mean annual salary of this sample was $39,000. At the 0.05 significance level, can we conclude that the mean annual salary of certified welders is less than $40,000? Complete steps 1 through 6 below.

Answer 1

Here we have to test that

Null hypothesis :

Alternative hypothesis :

where

This hypothesis test is left tailed test.

n = sample size = 200

Sample mean = 39000

Population standard deviation =   = 5200

Here population standard deviation is known so we use z test.

Test statistic :

z = -2.72 (Round to 2 decimal)

Test statistic = -2.72

P value:

Level of significance = = 0.05

Test is left tailed test.

P value = P(z < -2.72)

= 0.0033 (From statistical table of negative z values)

P value = 0.0033

Here p value <

So we reject H0

Conclusion : There is sufficient evidence to conclude that the mean annual salary of certified welders is less than $40,000