Question

An engineering firm is expanding its offices in the United States. The firm has selected four prime locations near major metropolitan areas. They want to determine if the average hourly wage is significantly different among the four chosen locations since this would impact overall cost. A survey of 20 wages of similar positions in each of the four locations was taken by random sampling, thus the sample size in each location was 5. The following ANOVA table was created based off the results of the study, let α = 0.05. Source of Variation SS df MS F Between Groups 95.28 3 31.76 4.3101 Within Groups 117.9 16 7.36875 Total 213.18 19 (a) Determine whether the following statement is true or false. It would be appropriate to perform the Tukey-Kramer (T-K) multiple comparisons procedure to identify differences in the means of the four locations. True False (b) The Tukey-Kramer method uses the formula (xi − xj) ± q MSE 2 1 ni + 1 nj . Using the formula, how many intervals will need to be calculated for this scenario to look at all pairwise comparisons for the study? (c) The Tukey-Kramer method uses the formula (xi − xj) ± q MSE 2 1 ni + 1 nj . Using the formula, what is the value of q from the table for this scenario? (Use a table.) (d) Consider the sample mean hourly wage for the four locations are: Location 1 = $42, Location 2 = $32, Location 3 = $37, Location 4 = $35. Are the mean hourly wages significantly different for Location 1 and Location 4? Yes No

Answer 1

The ANOVA table is,

ANOVA
Source of Variation	SS	df	MS	F
Between Groups	95.28	3	31.76	4.3101
Within Groups	117.9	16	7.36875
Total	213.18	19

a)

Determine whether the following statement is true or false. It would be appropriate to perform the Tukey-Kramer (T-K) multiple comparisons procedure to identify differences in the means of the four locations.

a)

Answer: TRUE

Explanation: The Tukey-Kramer (T-K) multiple comparisons procedure tests all the pairwise comparison and identify which pair is significantly different.

(b)

The Tukey-Kramer method uses the formula,

Where, k is the number of groups.

From the ANOVA table, k = 4,

(c)

The q value is obtained using the q distribution table for significance level = 0.05, number of groups, k = 4, degree of freedom = N - k = 20 - 4 = 16.

The HSD value is,

(d)

Mean hourly wages significantly different for Location 1 and Location 4 TRUE

Location	Mean
1	42
2	32
3	37
4	35

There are six possible comparison,

Comparison	Difference		HSD
	10	>	4.91177	Significant
	5	>	4.91177	Significant
	7	>	4.91177	Significant
	5	>	4.91177	Significant
	3	<	4.91177	Not significant
	2	<	4.91177	Not significant