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

Line 2020-10-20 Answered
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.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Bertha Stark
Answered 2020-10-21 Author has 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.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-11-01
Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.
If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?
asked 2021-03-02
In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference
asked 2022-02-26
Kirito is thinking of a number, if you add 7, multiply it by 6, subtract 18, and divide 2 theresult is 57. What is Kirito's number.
asked 2021-01-10
Effect of alcoholic parents A study1 compared personality characteristics between 49 children of alcoholics and a control group of 49 children of nonalcoholics who were matched on age and gender. On a measure of well being, the 49 children of alcoholics had a mean of 26.1(s=7.2) and the 49 subjects in the control group had a mean of [28.8(s=6.4)]. The difference scores between the matched subjects from the two groups had a mean of 2.7(s=9.7).
a. Are the groups to be compared independent samples or depentend samples? Why?
b. Show all speps of a test equality of the two population means for a two-sided alternative hypotesis. Report the P-value and interpret.
c. What assumptions must you make the inference in part b to be valid?
asked 2021-01-27
Prove an example of two independent samples and another example of dependent samples providing your reasoning To compare two means or two proportions, one works with two groups. The group are classfied either aas independent or matched pairs. Independent groups meam that the two samples taken are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs consist of two samples that are dependent. The parameter tested using matched pairs is the population mean. The parameters tested using independent groups are either population means or population proportion.
asked 2021-10-13
An IO psychologist is measuring the number of items a factory worker produces during the morning, afternoon or at night. What kind of test should be used on this data?
asked 2020-11-08
Give a ffull answer its true or false: When an ANOVA comparing the means of 3 groups indicates that at least one group is different from the others, a common follow-up analysis to determine which group(s) is (are) different is pairwise two-sample t-tests each assessed using i) the pooled standard deviation when calculating the standard error for the difference in means and ii) a Bonferonni-corrected alpha level of 0.0167 to control the type I error rate for the overall inference to 5%