Question

The types of browse favored by deer are shown in the following table. Using binoculars, volunteers observed the feeding habits of a random sample of 320 deer.

Type of
Browse |
Plant
Compositionin Study Area |
Observed
Number of DeerFeeding on This Plant |

Sage brush | 32% | 107 |

Rabbit brush | 38.7% | 121 |

Salt brush | 12% | 39 |

Service berry | 9.3% | 29 |

Other | 8% | 24 |

Use a 5% level of significance to test the claim that the natural distribution of browse fits the deer feeding pattern.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: The distributions are different.

*H*_{1}: The distributions are the
same.*H*_{0}: The distributions are the same.

*H*_{1}: The distributions are
different. *H*_{0}: The
distributions are the same.

*H*_{1}: The distributions are the
same.*H*_{0}: The distributions are different.

*H*_{1}: The distributions are different.

(b) Find the value of the chi-square statistic for the sample.
(Round the expected frequencies to at least three decimal places.
Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

YesNo

What sampling distribution will you use?

Student's
*t*uniform binomialnormalchi-square

What are the degrees of freedom?

(c) Estimate the *P*-value of the sample test statistic.

*P*-value > 0.1000.050 < *P*-value <
0.100 0.025 < *P*-value <
0.0500.010 < *P*-value < 0.0250.005 <
*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 that the population fits the
specified distribution of categories?

Since the *P*-value > *α*, we fail to reject
the null hypothesis.Since the *P*-value > *α*, we
reject the null hypothesis. Since the
*P*-value ≤ *α*, we reject the null hypothesis.Since
the *P*-value ≤ *α*, we fail to reject the null
hypothesis.

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

At the 5% level of significance, the evidence is sufficient to conclude that the natural distribution of browse does not fit the feeding pattern.At the 5% level of significance, the evidence is insufficient to conclude that the natural distribution of browse does not fit the feeding pattern.

Answer #1

The statistical software output for this problem is:

**Chi-Square goodness-of-fit results:**

Observed: Oi

Expected: Ei

N |
DF |
Chi-Square |
P-value |
---|---|---|---|

320 | 4 | 0.40055343 | 0.9824 |

Observed | Expected |
---|---|

107 | 102.4 |

121 | 123.84 |

39 | 38.4 |

29 | 29.76 |

24 | 25.6 |

Hence,

a) Level of significance = 0.05

Hypotheses: Option B is correct.

b) Test statistic = 0.401

Yes

Chi - square

Degrees of freedom = 4

c) P - value > 0.100

d) Option A is correct.

e) Option B is correct.

The types of browse favored by deer are shown in the following
table. Using binoculars, volunteers observed the feeding habits of
a random sample of 320 deer.
Type of Browse
Plant
Composition
in Study Area
Observed Number of
Deer
Feeding on This Plant
Sage brush
32%
110
Rabbit brush
38.7%
118
Salt brush
12%
44
Service berry
9.3%
23
Other
8%
25
Use a 5% level of significance to test the claim that the
natural distribution of browse fits the...

The types of browse favored by deer are shown in the following
table. Using binoculars, volunteers observed the feeding habits of
a random sample of 320 deer.
Type of Browse
Plant
Composition
in Study Area
Observed Number of
Deer
Feeding on This Plant
Sage brush
32%
103
Rabbit brush
38.7%
117
Salt brush
12%
46
Service berry
9.3%
29
Other
8%
25
Use a 5% level of significance to test the claim that the
natural distribution of browse fits the...

The types of browse favored by deer are shown in the following
table. Using binoculars, volunteers observed the feeding habits of
a random sample of 320 deer.
Type of Browse
Plant
Composition
in Study Area
Observed Number of
Deer
Feeding on This Plant
Sage brush
32%
107
Rabbit brush
38.7%
119
Salt brush
12%
41
Service berry
9.3%
26
Other
8%
27
Use a 5% level of significance to test the claim that the
natural distribution of browse fits the...

The types of browse favored by deer are shown in the following
table. Using binoculars, volunteers observed the feeding habits of
a random sample of 320 deer.
Type of Browse
Plant
Composition
in Study Area
Observed Number of
Deer
Feeding on This Plant
Sage brush
32%
98
Rabbit brush
38.7%
133
Salt brush
12%
40
Service berry
9.3%
29
Other
8%
20
Use a 5% level of significance to test the claim that the
natural distribution of browse fits the...

The types of browse favored by deer are shown in the following
table. Using binoculars, volunteers observed the feeding habits of
a random sample of 320 deer. Type of Browse Plant Composition in
Study Area Observed Number of Deer Feeding on This Plant Sage brush
32% 106 Rabbit brush 38.7% 123 Salt brush 12% 41 Service berry 9.3%
28 Other 8% 22 Use a 5% level of significance to test the claim
that the natural distribution of browse fits the...

The types of browse favored by deer are shown in the following
table. Using binoculars, volunteers observed the feeding habits of
a random sample of 320 deer. Type of Browse Plant Composition in
Study Area Observed Number of Deer Feeding on This Plant Sage brush
32% 108 Rabbit brush 38.7% 116 Salt brush 12% 47 Service berry 9.3%
28 Other 8% 21 Use a 5% level of significance to test the claim
that the natural distribution of browse fits the...

The types of browse favored by deer are shown in the following
table. Using binoculars, volunteers observed the feeding habits of
a random sample of 320 deer.
Type of Browse
Plant
Composition
in Study Area
Observed Number of
Deer
Feeding on This Plant
Sage brush
32%
99
Rabbit brush
38.7%
127
Salt brush
12%
43
Service berry
9.3%
28
Other
8%
23
Use a 5% level of significance to test the claim that the
natural distribution of browse fits the...

The director of library services at a college did a survey of
types of books (by subject) in the circulation library. Then she
used library records to take a random sample of 888 books checked
out last term and classified the books in the sample by subject.
The results are shown below.
Subject
Area
Percent of Books on
Subject in Circulation
Library on This Subject
Number of Books
in
Sample on This Subject
Business
32%
298
Humanities
25%
203
Natural...

The types of raw materials used to construct stone tools found
at an archaeological site are shown below. A random sample of 1486
stone tools were obtained from a current excavation site.
Raw
Material
Regional Percent of
Stone Tools
Observed Number of
Tools as Current excavation Site
Basalt
61.3%
912
Obsidian
10.6%
163
Welded Tuff
11.4%
176
Pedemal chert
13.1%
186
Other
3.6%
49
Use a 1% level of significance to test the claim that the
regional distribution of raw...

The director of library services at a college did a survey of
types of books (by subject) in the circulation library. Then she
used library records to take a random sample of 888 books checked
out last term and classified the books in the sample by subject.
The results are shown below.
Subject
Area
Percent of Books on
Subject in Circulation
Library on This Subject
Number of Books
in
Sample on This Subject
Business
32%
259
Humanities
25%
225
Natural...

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