Question

A random sample of 51 adult coyotes in a region of northern
Minnesota showed the average age to be *x* = 2.01 years,
with sample standard deviation *s* = 0.76 years. However, it
is thought that the overall population mean age of coyotes is
*μ* = 1.75. Do the sample data indicate that coyotes in this
region of northern Minnesota tend to live longer than the average
of 1.75 years? Use *α* = 0.01.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: *μ* < 1.75 yr;
*H*_{1}: *μ* = 1.75 yr*H*_{0}:
*μ* = 1.75 yr; *H*_{1}: *μ* < 1.75
yr *H*_{0}: *μ* >
1.75 yr; *H*_{1}: *μ* = 1.75
yr*H*_{0}: *μ* = 1.75 yr;
*H*_{1}: *μ* ≠ 1.75 yr*H*_{0}:
*μ* = 1.75 yr; *H*_{1}: *μ* > 1.75
yr

(b) What sampling distribution will you use? Explain the rationale
for your choice of sampling distribution.

The standard normal, since the sample size is large and
*σ* is unknown.The standard normal, since the sample size is
large and *σ* is known. The Student's
*t*, since the sample size is large and *σ* is
known.The Student's *t*, since the sample size is large and
*σ* is unknown.

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

(c) Estimate the *P*-value.

<*P*-value > 0.2500.100 < *P*-value <
0.250 0.050 < *P*-value <
0.1000.010 < *P*-value < 0.050*P*-value <
0.010

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* = 0.01 level, we reject the null hypothesis
and conclude the data are statistically significant.At the
*α* = 0.01 level, we reject the null hypothesis and conclude
the data are not statistically
significant. At the *α* = 0.01 level,
we fail to reject the null hypothesis and conclude the data are
statistically significant.At the *α* = 0.01 level, we fail
to reject the null hypothesis and conclude the data are not
statistically significant.

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

There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years

Answer #1

a)

0.01. is the level of significance

H0: μ = 1.75 yr; H1: μ > 1.75 yr

b)

The Student's t, since the sample size is large and σ is unknown.

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (2.01 - 1.75)/(0.76/sqrt(51))

t = 2.443

c)

P-value Approach

P-value = 0.0091

P-value < 0.010

As P-value < 0.01, reject the null hypothesis.

d)

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant

e)

There is sufficient evidence at the 0.01 level to conclude that
coyotes in the specified region tend to live longer than 1.75
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