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.

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:*

H_{0} : σ_{zoo = }σ_{wild}

That is, variances are equal.

*Alternative hypothesis:*

H_{1} : σ_{zoo > }σ_{wild}

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:

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 *H _{0.}*

If *p *- value > α, then fail to reject the null hypothesis *H _{0.}*

*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...

Tagged in

Q: How many ways can a dinner patron select 3 appetizers and 2 vegetables if there are 6 appetizers and...

A: Total number of available appetizers = 6Number of appetizers to be selected = 3Total number of avail...

Q: A manufacturer of a certain type of hardware has two manufacturing facilities and wants to compare t...

A: Conditions:The conditions for the two proportion test for sample sizes n1 and n2 with sample proport...

Q: Vocabulary for these terms • correlation • scatterplot • positive correlation • negative correlation...

A: Correlation: It is the linear relationship between the two variables. Scatterplot: It is the graph t...

Q: Nearly one half of americans aged 25 to 29 are unmarried. How large a sample is necessary to estima...

A: The formula for the sample size is as follows:

Q: Suppose that we have the data {x1, x2, ..., xn} such that x1=x2=...=xn=3. What is the mean of the da...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and r...

A: In this question, we have the weighs of adult wild mountain lions, which is681071251276064 Using tha...

Q: The Orchard Cafe has found that about 10% of the diners who make reservations don't show up. If 86 r...

A: The aim is to find the mean, µ, and standard deviation, σ of the binomial distribution.

Q: How do I solve this question with this table? obtain this sample using the portion of the random num...

A: By using random number table we can determine the random sampling with equal chance of occurrences o...

Q: Suppose you are assigned the number 1, and the other students in your statistics class call out cons...

A: Solution:(a) A random sample of four students from statistics class can be selected by using a compu...

Sorry about that. What wasn’t helpful?