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g Company A and Company B both produce a part used in a 3D Printer. A random sample of 9 parts from Company A results in a sample mean equal to 128.2 ft-lbs and a sample standard deviation 17.8 ft-lbs. A random sample of 8 parts from Company B gives a sample mean equal to 138.4 ft-lbs and a sample standard deviation 14.9 ft-lbs. If you do a test of hypothesis to see if the population variances of Company A and Company B parts are equal or not, what is the numerical value of the test statistic

Respuesta :

akiran007

Answer:

The value of test statistic is F =  1.427

Step-by-step explanation:

The given data is

n1=9;      s1=17.8

n2=8       s2=14.9

1) And significance level is chosen to be  α = 0.05.

2) The null and alternate hypothesis are

H0: σ₁²=σ₂²  against the claim Ha: σ₁²≠σ₂²

The null hypothesis the population variances of Company A and Company B parts are equal.

against the claim

the population variances are not equal of the  two companies.

3) The critical region F∝(υ1,υ2) = F(0.025)8,7 >  4.9

where υ1= n1-1= 9-1= 8 and υ2= n2-1= 8-1= 7

4)Test Statistic

F = s₁²/s₂²

F= 17.8²/ 14.9²=  1.427

5) Conclusion :

As the calculated F lies in the acceptance region therefore we conclude that there is not sufficient evidence to support the claim that the population variances of Company A and Company B parts are not equal. Hence Ha is rejected and H0 is accepted.