Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In

Question

Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it usually does. However, Jim sometimes gets chased out of the pasture by a bull that recovers too soon, and other times he becomes worried about prize bulls that take too long to recover. By reading journals, Jim has found that the tranquilizer should have a mean duration time of 65 minutes, with a standard deviation of 15 minutes. A random sample of 8 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of 22 minutes. At the 1% level of significance, is Jim justified in the claim that the variance is larger than that stated in his journal? Find a 90% confidence interval for the population standard deviation.

Explanation / Answer

a)

As given,

alpha = 0.01 [ANSWER]

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Formulating the null and alternative hypotheses,              
              
Ho:   sigma^2   =   225  
Ha:    sigma^2   >   225   [ANSWER, B]

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b)
  
As we can see, this is a    right   tailed test.  
Getting the test statistic, as              
s = sample standard deviation =    22          
sigmao = hypothesized standard deviation =    15          
n = sample size =    8          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    15.05777778   [ANSWER, TEST STATISTIC]

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df = N - 1 =    7   [ANSWER, DEGREES OF FREEDOM]      
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OPTION B: Normal distribution [ANSWER]

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c)  
              
As this is a right tailed test,

Pvalue = 0.035265869 [ANSWER]

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d)

As P > 0.01, we fail to reject Ho.

Hence,

OPTION B: Fail to reject Ho, not statistically significant. [ANSWER]

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e)

OPTION C: Fail to reject Ho, insufficient evidence. [ANSWER]
  

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