Question

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

In environmental studies, sex ratios are of great importance.
Wolf society, packs, and ecology have been studied extensively at
different locations in the U.S. and foreign countries. Sex ratios
for eight study sites in northern Europe are shown below.

Location of Wolf Pack % Males (Winter) %
Males (Summer)

Finland 74 57

Finland 60 67

Finland 64 45

Lapland 55 48

Lapland 64 55

Russia 50 50

Russia 41 50

Russia 55 45

It is hypothesized that in winter, "loner" males (not present in
summer packs) join the pack to increase survival rate. Use a 5%
level of significance to test the claim that the average percentage
of males in a wolf pack is higher in winter. (Let d = winter −
summer.)

(a) What is the level of significance?

State the null and alternate hypotheses. Will you use a
left-tailed, right-tailed, or two-tailed test?

H0: μd = 0; H1: μd > 0; right-tailed

H0: μd = 0; H1: μd ≠ 0; two-tailed

H0: μd > 0; H1: μd = 0; right-tailed

H0: μd = 0; H1: μd < 0; left-tailed

(b) What sampling distribution will you use? What assumptions
are you making?

The standard normal. We assume that d has an approximately uniform
distribution.

The Student's t. We assume that d has an approximately normal
distribution.

The standard normal. We assume that d has an approximately normal
distribution.

The Student's t. We assume that d has an approximately uniform
distribution.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) the P-value.

P-value > 0.250

0.125 < P-value < 0.250

0.050 < P-value < 0.125

0.025 < P-value < 0.050

0.005 < P-value < 0.025

P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject
or fail to reject the null hypothesis? Are the data statistically
significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude
the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and
conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude
the data are not statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and
conclude the data are not statistically significant.

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

Reject the null hypothesis, there is insufficient evidence to claim
that the average percentage of male wolves in winter is
higher.

Reject the null hypothesis, there is sufficient evidence to claim
that the average percentage of male wolves in winter is
higher.

Fail to reject the null hypothesis, there is insufficient evidence
to claim that the average percentage of male wolves in winter is
higher.

Fail to reject the null hypothesis, there is sufficient evidence to
claim that the average percentage of male wolves in winter is
higher.

Answer #1

a)

0.05 is alpha

H0: μd = 0; H1: μd > 0; right-tailed

b)

The Student's t. We assume that d has an approximately normal distribution.

Test statistic,

t = (dbar - 0)/(s(d)/sqrt(n))

t = (5.75 - 0)/(10.3199/sqrt(8))

t = 1.576

c)

P-value Approach

P-value = 0.0795

0.050 < P-value < 0.125

d)

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

e)

Fail to reject the null hypothesis, there is insufficient
evidence to claim that the average percentage of male wolves in
winter is higher

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom d.f. not in the
Student's t table, use the closest d.f. that is smaller. In some
situations, this choice of d.f. may increase the P-value by a small
amount and therefore produce a slightly more "conservative" answer.
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approximately normal. Note: For degrees of freedom
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the closest d.f. that is smaller. In
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the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
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the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
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approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that
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d.f. may increase the P-value by a small
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approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
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approximately normal. Note: For degrees of freedom
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the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
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