Question

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.)

Answer 1

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:-

$F=\frac{MSB}{MSE}$

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.