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 12 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of 24 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 95% confidence interval for the population standard deviation.

(a) What is the level of significance?

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?

(f) Find the requested confidence interval for the population standard deviation. (Round your answers to two decimal place.)

lower limit
upper limit

Answer 1

Here by the problem,

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 n=12 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of 24 minutes. Now at the 1% level of significance, we want to test whether Jim is justified in the claim that the variance is larger than that stated in his journal

(a) Here the level of significance be 0.01

(b) Now if be the actual population standard deviation then the hypotheses be,

Here in order to test that the test statistic be,

where s be the sample standard deviation

Here putting the values we get,

And the degrees of freedom be n-1=11

(f) Now the requested confidence interval for the population standard deviation be,

where be the upper 0.025 point of chi suare distribution with df 11. Similarly,

Putting the values we get, the confidence intervl as,

Hence the answer..............

Thank you...............