Question

A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow Employee I 23, 27, 29 30, 27, 25 18, 20, 22 II 25,26 24 24,29, 26 19, 16 14 28,25 26 25,27,23 15, 11, 17 Machine ?1 ANALYSIS OF VARIANCE ITEMS SOURCE DF SS MS 2 3467 1733 EMPLOYEE 2 50467 252.33 INTERACTION 4 2667 6.6 ERROR TOTAL 18 98.00 544 26 664.00 Using a 0.05 significance level, test the claim that the interaction between employee and machine has no effect on the number of items produced. Calculate the F-statistic for this test. Round your answer to four decimal places. A) 2.9300 B) 2.9277 C) 0.0687 D) 49.5699 E) 1.2261 Save

Answer 1

Option E) is correct.

Explanation:

The hypothesis for the interaction between two factor machine and employee is defined as,

Null hypothesis: There is no interaction present between two factor.

Alternate hypothesis: There is a significant interaction present between two factor.

The F-statistic for interaction is obtained as,

The P-value for F statistic is obtained using the F distribution table for numerator degree of freedom = 4 and denominator degree of freedom = 18.

$F_{\alpha,df1,df2}=F_{0.05,4,18}=\boldsymbol{1.226103}$

The P-value is greater than 0.05 at 5% significance hence the null hypothesis is rejected. THere is no interaction present between two factor machine and employee.