Jim Mead is a veterinarian who visits a Vermont farm to examineprize bulls. In order to examine a bull, Jim first gives the animala tranquilizer shot. The effect of the shot is supposed to last anaverage of 65 minutes, and it usually does. However, Jim sometimesgets chased out of the pasture by a bull that recovers too soon,and other times he becomes worried about prize bulls that take toolong to recover. By reading journals, Jim has found that thetranquilizer should have a mean duration time of 65 minutes, with astandard deviation of 15 minutes. A random sample of 14 of Jim'sbulls had a mean tranquilized duration time of close to 65 minutesbut a standard deviation of 22 minutes. At the 1% level ofsignificance, is Jim justified in the claim that the variance islarger than that stated in his journal? Find a 95% confidenceinterval for the population standard deviation.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ² = 225;H₁: σ² <225

H_o: σ² = 225;H₁: σ² ≠225    

H_o: σ² >225; H₁: σ² =225

H_o: σ² = 225;H₁: σ² >225

(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?

What assumptions are you making about the originaldistribution?

We assume a exponential population distribution.

We assume a binomial populationdistribution.    

We assume a normal population distribution.

We assume a uniform population distribution.

(c) Find or estimate the P-value of the sample teststatistic.

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

(d) Based on your answers in parts (a) to (c), will you rejector fail to reject the null hypothesis?

Since the P-value > α, we fail to rejectthe null hypothesis.

Since the P-value > α, we reject the nullhypothesis.    

Since the P-value ≤ α, we reject the nullhypothesis.

Since the P-value ≤ α, we fail to reject thenull hypothesis.

(e) Interpret your conclusion in the context of theapplication.

At the 1% level of significance, there is insufficient evidenceto conclude that the variance of the duration times of thetranquilizer is larger than stated in the journal.

At the 1% level of significance, there is sufficient evidence toconclude that the variance of the duration times of thetranquilizer is larger than stated in thejournal.    

(f) Find the requested confidence interval for the populationstandard 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 σ lies above thisinterval.

We are 95% confident that σ lies outside thisinterval.    

We are 95% confident that σ lies below thisinterval.

We are 95% confident that σ lies within thisinterval.