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 25 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? Correct: Your answer is correct. State the null and alternate hypotheses. Ho: ?2 = 225; H1: ?2 > 225 Ho: ?2 > 225; H1: ?2 = 225 Ho: ?2 = 225; H1: ?2 < 225 Ho: ?2 = 225; H1: ?2 ? 225 Correct: Your answer is correct. (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) Correct: Your answer is correct. What are the degrees of freedom? Correct: Your answer is correct. What assumptions are you making about the original distribution? We assume a uniform population distribution. We assume a exponential population distribution. We assume a normal population distribution. We assume a binomial population distribution. Correct: Your answer is correct. (c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005 Correct: Your answer is correct. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value > ?, we fail to reject the null hypothesis. Since the P-value > ?, we reject the null hypothesis. Since the P-value ? ?, we reject the null hypothesis. Since the P-value ? ?, we fail to reject the null hypothesis. Correct: Your answer is correct. (e) Interpret your conclusion in the context of the application. At the 1% level of significance, there is insufficient evidence to conclude that the variance of the duration times of the tranquilizer is larger than stated in the journal. At the 1% level of significance, there is sufficient evidence to conclude that the variance of the duration times of the tranquilizer is larger than stated in the journal. Correct: Your answer is correct. (f) Find the requested confidence interval for the population standard deviation. (Round your answers to two decimal place.) lower limit min upper limit min Interpret the results in the context of the application. We are 95% confident that ? lies outside this interval. We are 95% confident that ? lies within this interval. We are 95% confident that ? lies below this interval. We are 95% confident that ? lies above this interval.

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.

Now a random sample of n=8 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of s=25 minutes.

Now at the 1% level of significance, we want to test the claim that the variance is larger than that stated in his journal

(a) Here the level of significance is 0.01

Now the null and alternate hypotheses be

(b) So in order to test that the chi-square statistic for the sample be,

where under Ho,

now putting the values we get,

Here the degrees of freedom is n-1=7

Now in order to test that we assumed distribution about the population is

We assume a normal population distribution.

(c) Now the P-value of the sample test statistic be,

Now we note that,

0.005 < P-value < 0.010

(d) Based the answers in parts (a) to (c),

since the , we reject the null hypothesis.

(e) Interpretation:

At the 1% level of significance, there is sufficient evidence to conclude that the variance of the duration times of the tranquilizer is larger than stated in the journal.

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

where be the upper 0.025 point of chi square distribution with df n-1=7

Now here we have,

Now putting the values we get that,

Here lower limit is 16.53 and upper limit is 50.88

Interpretation

We are 95% confident that lies within this interval.

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

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