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 each. the resulting sample average is 671.13. assuming a population standard deviation of 63.90 and a 10% level significance, determine whether the mean weekly earnings of a production worker have changed.

The value of the test statistics is

Answer 1

according to u.s. bureau of labor statistics, the average weekly earnings of a production worker in July 2011 were = 657.49.

and the researcher randomly selects n = 55 production workers from across the united states and obtains a representative earnings statement for one week each. the resulting sample average is = 671.13. assuming a population standard deviation of = 63.90 and a 10% level significance

So, based on the Labor researcher the hypotheses we create are:

Based on the hypothesis it will be a two-tailed test.

Rejection region:

Based on the significance level and type of hypothesis test the critical value is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.95) this results in Z =+/-1.645

So, reject Ho if -Z <-1.645 or Z> 1.645

Test Statistic:

P-value:

P-value is calculated using excel formula for normal distribution at calculated Z score, the formula is =2*(1-NORM.S.DIST(1.583, TRUE))

this results in P-value = 0.1134

Conclusion:

Since the P-value is larger than 0.10 and Z > Zc hence at 0.10 level of significance we failed to reject the null hypothesis and conclude that there is insufficient evidence to warrant the claim that figure is still accurate today