Suppose you are testing whether the lifetime of 4 different types of lightbulbs. You run 5 experiments each. You get a mean square error of MS_{E}=1.7

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Answered question

2020-10-20

Suppose you are testing whether the lifetime of 4 different types of lightbulbs. You run 5 experiments each. You get a mean square error of MSE=1.75 and you reject the null hypothesis. The sample means you obtain for each lightbulb are below:
Type 1: 20
Type 2: 30
Type 3: 28
Type 4: 22
Which pairs are significantly different at the 5% significance level? Select all that apply.

Answer & Explanation

Bertha Stark

Bertha Stark

Skilled2020-10-21Added 96 answers

Step 1
From the provided data we have,
MSE=1.75
dft=4 × 5=20
dfw=20  4=16
k= number of groups =4
Type 1Type 2Type 3Tepe 420302822
Step 2
Using Tukey’s HSD:
We first compute the Tukey’s HSD as below:
D=qα, k, dfw MSEn
=4.046 1.755 (from studentized q - table)
=2.393646
(Where n represent the number of observations in each group).
The absolute differences in group means is computed as below:
Groups|Differences in group means|1210138142232248346
We say that the groups are significantly only when the absolute difference in group mean is larger than the HSD value.
Thus, this difference is larger for Group 1 and 2, Group 1 and 3, Group 2 and 4 and Group 3 and 4
Thus, the pairs that are significantly different at the 5% significance level are,
Type 1-2Type 1-3Type 2-4Type 3-4
and other groups are not significant.

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