The American Carbon Registry, www.americancarbonregistry.org, provides approved

Question

The American Carbon Registry, www.americancarbonregistry.org, provides approved measurement methodologies for energy companies who wish to show greenhouse gas emission reduction through retrofitting high-bleed pneumatic controllers with low-bleed controllers. Summary sample data from the two manufacturers are shown in the table below. Are the variances of the two manufacturers equal?

s2 = 237.9             

Choose the appropriate hypotheses. Assume 12 is the variance of the manufacturer Cemco and 22 is the variance of the manufacturer Invalco.

Calculate the critical values for = 0.10. (Round your answers to 3 decimal places.)

  

                     s1 = 147.2            

s2 = 237.9             

a)

Choose the appropriate hypotheses. Assume 12 is the variance of the manufacturer Cemco and 22 is the variance of the manufacturer Invalco.

a. H0: 12 / 22 = 1vs. H1: 12 / 22 1 b. H0: 12 / 22 1vs. H1: 12 /22 = 1 a b (b)

Calculate the critical values for = 0.10. (Round your answers to 3 decimal places.)

     FR   FL (c) Calculate the test statistic Fcalc. (Round your answer to 3 decimal places.)
  Fcalc (d) What is your conclusion?

  

  We (Click to select)cancannot conclude that the variances are not equal n1 = 18                 n2 = 17                 

Explanation / Answer

Here we are given that,

X1bar = 510.5

X2bar = 628.9

s1 = 147.2

s2 = 237.9

n1 = 18

n2 = 17

Choose the appropriate hypotheses. Assume 12 is the variance of the manufacturer Cemco and 22 is the variance of the manufacturer Invalco.

H0: 12 / 22 = 1 vs. H1: 12 / 22 1

Option a) is correct.

Calculate the critical values for = 0.10.

= 0.10.

Critical value in F distribution we can find by using EXCEL.

syntax :

=FINV(probability, deg_freedom1, deg_freedom2)

probability = alpha/2

deg_freedom1 = n2-1 = 17-1 = 16

deg_freedom2 = n1-1 = 18-1 = 17

Critical value = 2.289

Calculate the test statistic Fcalc

Fcalc = largest variance / smallest variance

= s22 /s12

= 237.92 / 147.22

= 2.612

What is your conclusion?

Fcalc > critical value

Reject H0 at 10% level of significance.

Conclusion : The two variances are not equal.

a)

Choose the appropriate hypotheses. Assume 12 is the variance of the manufacturer Cemco and 22 is the variance of the manufacturer Invalco.

H0: 12 / 22 = 1 vs. H1: 12 / 22 1

Option a) is correct.

(b)

Calculate the critical values for = 0.10.

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