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 55 production workers from across the United States and obtains a representative earnings statement for one week from each. The resulting sample average is $672.84. Assuming a population standard deviation of $63.90 and a 5% level of significance, determine whether the mean weekly earnings of a production worker have changed.

Appendix A Statistical Tables

(Round your answer to 2 decimal places.)

The value of the test statistic is ______________________ and we _______________________ (reject the null hypothesis or fail to reject the null hypothesis.)

Answer 1

Null hypothesis      

   
          
Alternative hypothesis      

   
          
We have given,          
Population mean for given example =$657.49  
Sample mean=$672.84  
Population standard deviation =   $63.9  
Sample size for given example =   55  
Level of significance =0.05  
Z test statistic formula

  
=1.78  

P value =0.0751.....................by using Z table or Excel command =2*(1-NORMSDIST(1.78))

P value > 0.05

The value of the test statistic is 1.78 and we fail to reject the null hypothesis.