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7.18A wildlife biologist was interested in determining the effect of raising deer in captivity on the size of the deer. She decided to consider three populations: deer raised in the wild, deer raised on large hunting ranches, and deer raised in zoos. She randomly selected eight deer in each of the three environments and weighed the deer at age 1 year. The weights (in pounds) are given in the following table.Environment                        Weight (in pounds) of DeerWild114.7128.9111.5116.4134.5126.7120.6129.59Ranch120.491.0119.6119.4150.0169.7100.976.1Zoo103.190.7129.575.8182.576.887.377.3a. The biologist hypothesized that the weights of deer from captive environments would have a larger level of variability than the weights from deer raised in the wild. Do the data support her contention?b. Are the requisite conditions for the test you used in part (a) satisfied in this situation? Provide plots to support your answer.

Question

7.18

A wildlife biologist was interested in determining the effect of raising deer in captivity on the size of the deer. She decided to consider three populations: deer raised in the wild, deer raised on large hunting ranches, and deer raised in zoos. She randomly selected eight deer in each of the three environments and weighed the deer at age 1 year. The weights (in pounds) are given in the following table.

Environment                        Weight (in pounds) of Deer

Wild 114.7 128.9 111.5 116.4 134.5 126.7 120.6 129.59
Ranch 120.4 91.0 119.6 119.4 150.0 169.7 100.9 76.1
Zoo 103.1 90.7 129.5 75.8 182.5 76.8 87.3 77.3


a. The biologist hypothesized that the weights of deer from captive environments would have a larger level of variability than the weights from deer raised in the wild. Do the data support her contention?

b. Are the requisite conditions for the test you used in part (a) satisfied in this situation? Provide plots to support your answer.

check_circleAnswer
Step 1

a.

The biologist claimed that the weights of deer from captive environments have larger variability than the weights from deer raised in wild.

The captive environment is Zoo.

Hence, the variance test can be done on zoo and wild.

Null hypothesis:

H0 : σzoo =  σwild

That is, variances are equal.

Alternative hypothesis:

H1 : σzoo >  σwild

That is, the standard deviation for zoo is more than the standard deviation for wild.

Test statistic:

Software procedure:

Step-by-step procedure to obtain the test statistic using MINITAB software is given below:

 

  • Choose Stat > Basic Statistics > 2 Variance.
  • Under Data, choose Samples in different columns.
  • In First, enter
  • In second, enter
  • Check Options, enter Confidence level as 0.
  • Choose greater that in alternative.
  • Click OK in all dialog boxes.

The output using the MINITAB software is given below:

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Step 2

From the MINITAB output, the value of the F test statistic is 20.40 and the p-value is 0.

α = 0.05 is the level of significance

Decision:

If p - value ≤  α, then reject the null hypothesis H0.

If p - value > α, then fail to reject the null hypothesis H0.

Conclusion:

The p-value is less than the level of significance.

That is, 0 < 0.05.

By the rejection rule, reject the null hypothesis.

Therefore,

There is proper evidence to say that there is variability between zoo and wild deer.

Hence, the data supports the contention.

 

Step 3

b.

For using the test, the populations should be normally distributed and the data sho...

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