A new operator was recently assigned to a crew of workers who perform a certain job. From the records of the number of units of work completed by each worker each day last month, a sample of size five was randomly selected for each of the two experienced workers and the new worker. At the α = .05 level of significance, does the evidence provide sufficient reason to reject the claim that there is no difference in the amount of work done by the three workers?
Workers | |||
New | A | B | |
Units of work (replicates) | 9 | 10 | 11 |
8 | 12 | 9 | |
10 | 10 | 11 | |
9 | 11 | 12 | |
9 | 12 | 9 |
(a) Find the test statistic. (Give your answer correct to two
decimal places.)
(ii) Find the p-value. (Give your answer bounds
exactly.)
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u1 = u2 = u3
Alternative hypothesis: At-least one of the u is not equal.
Formulate an analysis plan. For this analysis, the significance level is 0.05.
Analyze sample data.
F statistics is given by:-
F = 4.79
The P-value = 0.0296.
0.025 < p-value < 0.05.
Interpret results. Since the P-value (0.0296) is less than the significance level (0.05), we have to reject the null hypothesis.
Conclusion:-
Reject H0, There is sufficient evidence for significant difference in the amount of work done by the three workers.
A new operator was recently assigned to a crew of workers who perform a certain job....
A new operator was recently assigned to a crew of workers who perform a certain job. From the records of the number of units of work completed by each worker each day last month, a sample of size five was randomly selected for each of the two experienced workers and the new worker. At the α = .05 level of significance, does the evidence provide sufficient reason to reject the claim that there is no difference in the amount of...
A new operator was recently assigned to a crew of workers who perform a certain job. From the records of the number of units of work completed by each worker each day last month, a sample of size five was randomly selected for each of the two experienced workers and the new worker. At the α = .05 level of significance, does the evidence provide sufficient reason to reject the claim that there is no difference in the amount of...
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