Question

In: Statistics and Probability

According the Ministry of Labour statistics, the average weekly earnings of a factory worker last year...

According the Ministry of Labour statistics, the average weekly earnings of a factory worker last year were $424.20. Suppose a labour researcher wants to determine whether these figures are still accurate this year. The researcher randomly selects 60 workers. The sample mean is $435.70 with a standard deviation of $33. Taking a level of significance of 3%, determine whether the mean weekly earnings of a factory worker have changed.

Solutions

Expert Solution

Solution :

According to the Ministry of Labor statistics, the average weekly earnings of a factory worker last year were $424.20. It is supposed that a labor researcher wants to determine whether these figures are still accurate this year. The researcher randomly selects 60 workers with the sample mean is $435.70 and a standard deviation of $33. Taking a level of significance of 3%, we have to determine whether the mean weekly earnings of a factory worker have changed !

The appropriate null and alternative hypotheses are :

Since, here, the Sample Size = 60 > 30 , we can use the 1 - Sample Z Test to test the above hypothesis.

Thus , the appropriate test statistic is given as,


From the data given , we have the following information :

Thus , the value of the test statistic is given as,

The p - value of the test is given as,

Decision from the test hypothesis test using = 0.04 level of significance :

Conclusion : Since clearly , the p - value of the test is less than the level of significance () for the above test , thus we REJECT the Null Hypothesis at = 3% level of significance and conclude on the basis of the given data that the mean weekly earnings of a factory worker have changed with respect to the last year ........................... (Ans)

______________________________


Related Solutions

according to the u.s. bureau of labor statistics, the average weekly earnings of a production worker...
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...
According to the Bureau of Labor Statistics (BLS), the mean weekly earnings of salary workers in...
According to the Bureau of Labor Statistics (BLS), the mean weekly earnings of salary workers in the United States in 2018 was µ =$870. Assume that the weekly earnings are approximately normally distributed with a standard deviation of σ = $90. If a salary worker is selected at random, what is the probability that his/her weekly earnings exceed $700? What are the weekly earnings for which 95% of salary workers’ earnings are in this range? What is the weekly earning...
In 2003, the average weekly earnings of truck drivers was $603 while average weekly earnings of...
In 2003, the average weekly earnings of truck drivers was $603 while average weekly earnings of bank tellers was only $395. How might market, institutional, and sociological forces, respectively, be responsible for the higher earnings of truck drivers? 6 MARKS
Suppose that a recent issue of a magazine reported that the average weekly earnings for workers...
Suppose that a recent issue of a magazine reported that the average weekly earnings for workers who have not received a high school diploma is $495. Suppose you would like to determine if the average weekly for workers who have received a high school diploma is significantly greater than average weekly earnings for workers who have not received a high school diploma. Data providing the weekly pay for a sample of 50 workers are available in the file named WeeklyHSGradPay....
Suppose that a recent issue of a magazine reported that the average weekly earnings for workers...
Suppose that a recent issue of a magazine reported that the average weekly earnings for workers who have not received a high school diploma is $496. Suppose you would like to determine if the average weekly for workers who have received a high school diploma is significantly greater than average weekly earnings for workers who have not received a high school diploma. Data providing the weekly pay for a sample of 50 workers are available in the file named WeeklyHSGradPay....
Suppose that a recent issue of a magazine reported that the average weekly earnings for workers...
Suppose that a recent issue of a magazine reported that the average weekly earnings for workers who have not received a high school diploma is $498. Suppose you would like to determine if the average weekly for workers who have received a high school diploma is significantly greater than average weekly earnings for workers who have not received a high school diploma. Data providing the weekly pay for a sample of 50 workers are available in the file named WeeklyHSGradPay....
38 According to current stats, the average women's earnings as a percent of men's earnings is...
38 According to current stats, the average women's earnings as a percent of men's earnings is highest in the grouping of: a. Caucasian or white ethnicity b. African American ethnicity c. Asian ethnicity d. Hispanic or Latino ethnicity
A shoe factory in Athens sells shoes for $50 per pair. The last worker hired produced...
A shoe factory in Athens sells shoes for $50 per pair. The last worker hired produced an additional 8 pairs of shoes, and was paid $100 per hour. (a) Should the rm hire more workers, re some workers, or keep the same number of workers? Explain why. (b) Suppose one of the factory's machines breaks and cannot be replaced. Comment on how this will aect the productivity of each worker, and how this would aect the hiring decision of the...
According to a Human Resources report, a worker in the industrial countries spends on average 419...
According to a Human Resources report, a worker in the industrial countries spends on average 419 minutes a day on the job. Suppose the standard deviation of time spent on the job is 28 minutes. a. If the distribution of time spent on the job is approximately bell shaped, between what two times would 68% of the figures be? enter the lower limit for the interval where 68% of the values would fall 391 to enter the upper limit for...
According to a Human Resources report, a worker in the industrial countries spends on average 419...
According to a Human Resources report, a worker in the industrial countries spends on average 419 minutes a day on the job. Suppose the standard deviation of time spent on the job is 25 minutes. a. If the distribution of time spent on the job is approximately bell shaped, between what two times would 68% of the figures be? enter the lower limit for the interval where 68% of the values would fall  to enter the upper limit for the interval...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT