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A manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference between the two processes. A summary of the findings is shown next.

What is the critical value of F at the 1% level of significance?
a. 9.46
b. 8.29
c. 8.18
d. 4.61

A manufacturer of automobile transmissions uses two different processes Management ordered a study of the production costs to see if there is a difference betwe class=

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cchilabert

Answer:

b. 8.29

Step-by-step explanation:

Hello!

The objective is to study both processes to see if there is any difference between the costs of manufacturing.

An ANOVA was conducted for the variable:

Y: cost of manufacturing automobile transmissions

Factor: Process

Treatments: 1 and 2

The statistic for this test is

[tex]F= \frac{MS_{Treatment}}{MS_{Error}} ~~F_{k-1; n-k}[/tex]

Where

k= number of treatments

n= total number of observations

Degrees of freedom of the treatments: k-1= 2-1= 1

Degrees of freedom of errors: n-k= 20-2= 18

The critical region for this analysis is always one tailed to the right.

[tex]F_{k-1;n-k;1-\alpha }= F_{1;18;0.90}= 8.28[/tex]

I hope this helps!

fichoh

Using the F distribution and the appropriate degree of freedom values, the critical value of F at 0.1 is 8.29

From the table attached :

  • Number of treatment, k = 2

  • Total number of observations, n = 20

  • α = 0.1

The Fcritical value can be defined thus :

[tex] F_{df \: treatment, \: df \: error, 1 - α} [/tex]

  • df treatment, degree of freedom of treatment = k - 1 = 2 - 1 = 1

  • df error, degree of freedom of error = n - k = 20 - 2 = 18

Using the F distribution or calculator :

  • [tex] F_{df \: treatment, \: df \: error, 1 - α} = F_{1, 18, 0.9} = 8.29 [/tex]

Hence, the critical value of F at 0.1 is 8.29

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