In: Statistics and Probability
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.
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)
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