An auto manufacturing company wants to estimate the variance of miles per gallon

Question

An auto manufacturing company wants to estimate the variance of miles per gallon for its auto model AST72. A random sample of 24 cars of this model showed that the standard deviation of miles per gallon is 0.58. Research department would like to determine if the sample result indicates that the population variance is decreased from historical value of 0.35. At alpha = 1%, give values for test and critical statistics

Select one:

A. c2test=41.638 and c2critical=22.1063

B. c2test=22.1063 and c2critical=41.638

C. c2test=10.196 and c2critical=22.1063

D. c2test=22.1063 and c2critical=10.196

An auto manufacturing company wants to estimate the variance of miles per gallon for its auto model AST72. A random sample of 24 cars of this model showed that the standard deviation of miles per gallon is 0.58. At the alpha = 1%, can the research department conclude that the population variance of miless per gallon for AST72 is decreased from historical value of 0.35?

Select one:

A. At alpha = 1%, they reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35.

B. At alpha = 1%, they failed to reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35.

C. At alpha = 1%, they failed to reject the null hypothesis. The variance of miles per gallon for AST72 model has decreased from the historical value of 0.35.

D. At alpha = 1%, they reject the null hypothesis. The variance of miles per gallon for AST72 model has not decreased from the historical value of 0.35.

Explanation / Answer

1.

1.

As

df = N - 1 =    23

Then at 0.01 left tailed test,

chi^2 (crit) =    10.19571556

Getting the test statistic, as  
s = sample standard deviation =    0.58
sigmao = hypothesized standard deviation = SQRT(0.35) =   0.591607978
n = sample size =    24

Thus, chi^2 = (N - 1)(s/sigmao)^2 =    22.10628571

Hence,

OPTION D. c2test=22.1063 and c2critical=10.196 [ANSWER]

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