Question

a.

A production manager was testing three different methods of production. Each method was assigned to a randomly selected set of workers (five each), and their time for the task completion was recorded (given below). The observations are independent, each population has the same variance, and are Normally distributed.

Method A	Method B	Method C
58	58	48
64	69	57
55	71	59
66	64	47
67	68	49

We need to conduct an ANOVA test with the following hypotheses:

H0: the three population means are equal

H1: the three population means are not all equal

Test at 5% level of significance.

For this data, what is the F-statistic ( = MSwithin / MSbetween, also written as MSerror/MScolumns; here MS stands for mean square)?

(You may copy the data and use Excel or StatCrunch to compute the result)

(Provide two decimal places)___________

B.

A production manager was testing three different methods of production. Each method was assigned to a randomly selected set of workers (five each), and their time for the task completion was recorded (given below). The observations are independent, each population has the same variance, and are Normally distributed.

Method A	Method B	Method C
58	58	48
64	69	57
55	71	59
66	64	47
67	68	49

We need to conduct an ANOVA test with the following hypotheses:

H0: the three population means are equal

H1: the three population means are not all equal

Test at 5% level of significance.

For this test, what is the F critical value?

(You may copy the data and use Excel or StatCrunch to compute the result)

(Provide two decimal places)__

C.

A production manager was testing three different methods of production. Each method was assigned to a randomly selected set of workers (five each), and their time for the task completion was recorded (given below). The observations are independent, each population has the same variance, and are Normally distributed.

Method A	Method B	Method C
58	58	48
64	69	57
55	71	59
66	64	47
67	68	49

We need to conduct an ANOVA test with the following hypotheses:

H0: the three population means are equal

H1: the three population means are not all equal

Test at 5% level of significance.

What is the conclusion of this test?

		sample means are not all equal
		population means are equal (i. e. we have no evidence against it)
		population means are not all equal
		sample means are equal (i. e. we have no evidence against it)

Answer 1

Given that a production manager was testing three different methods of production.

We need to conduct an ANOVA test with the following hypotheses:

H0: the three population means are equal

H1: the three population means are not all equal

The results of the anova test conducted in EXCEL is given below.

A. from the results of the ANOVA as provided above . The value of the test statistic is 9.18

B. TheF critical value is 3.89

C. conclusion of the test:

since the calculated F value is greater than F critical value at 5% level of significance so we reject the null hypothesis and conclude that population means are not all equal.