(i) 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 of10of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of25minutes. At the 1% level of significance, is Jim justified in the claim that the variance is larger than that stated in his journal?

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

(b) What assumptions are you making about the original distribution?

• We assume a exponential population distribution.
• We assume a binomial population distribution.
• We assume a normal population distribution.
• We assume a uniform population distribution.

(c) Find or estimate theP-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

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

• Since theP-value >, we fail to reject the null hypothesis.
• Since theP-value >, we reject the null hypothesis.
• Since theP-value, we reject the null hypothesis.
• Since theP-value, we fail to reject the null hypothesis.

(ii) A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance²of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of²= 23 months (squared) is most desirable for these batteries. A random sample of20batteries gave a sample variance of12.8months (squared). Using a 0.05 level of significance, test the claim that²= 23 against the claim that²is different from 23.

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

(b) What assumptions are you making about the original distribution?

• We assume a binomial population distribution.
• We assume a exponential population distribution.
• We assume a normal population distribution.
• We assume a uniform population distribution.

(c) Find or estimate theP-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

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

• Since theP-value >, we fail to reject the null hypothesis.
• Since theP-value >, we reject the null hypothesis.
• Since theP-value, we reject the null hypothesis.
• Since theP-value, we fail to reject the null hypothesis.