What would the Tukey test value be for comparing the means of machine B and machine C at $a = 0.05$ ?
A) -1.61
B) -1.17
C) -7.72
D) -4.46

Question

Quizplus · Accepted Answer

The Tukey test value for comparing the means of machine B and machine C can be calculated as:

Tukey test value = (mean of machine B - mean of machine C) / standard error

From the information given in the table, we have:

mean of machine B = 80
mean of machine C = 93
standard error = 2.81 (calculated using the formula: standard error = square root of (mean square within / sample size), where mean square within and sample size can be found in the ANOVA table)

Thus, the Tukey test value = (80 - 93) / 2.81 = -4.46

At a significance level of 0.05, the critical value for the Tukey test with 6 degrees of freedom for the error term is 3.055. Since -4.46 is less than -3.055, we can conclude that the difference between the means of machine B and machine C is statistically significant. Therefore, the best choice is D.

What Would the Tukey Test Value Be for Comparing the Means