Question

According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in July 2011 were $657.49. Suppose a labor researcher wants to test to determine whether this figure is still accurate today. The researcher randomly selects 53 production workers from across the United States and obtains a representative earnings statement for one week from each. The resulting sample average is $670.16. Assuming a population standard deviation of $63.90 and a 10% level of significance, determine whether the mean weekly earnings of a production worker have changed.

Answer 1

H0: = 657.49,

Ha: 657.49

Test statistics

z = - / / sqrt(n)

= 670.16 - 657.49 / 63.90 / sqrt(53)

= 1.44

This is test statistics value.

p-value = 2 * P( Z > z)

= 2 * P( Z > 1.44)

= 2 * 0.0749

= 0.1498

Since p-value > 0.10 level, we do not have sufficient evidence to reject H0.

We conclude at 0.10 level that we fail to support the claim.