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
years.

A random sample of 51 adult coyotes in a region of northern
Minnesota showed the average age to be x = 1.99 years,
with sample standard deviation s = 0.70 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...

A random sample of 51 adult coyotes in a region of northern
Minnesota showed the average age to be x = 2.03 years,
with sample standard deviation s = 0.80 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...

A random sample of 46 adult coyotes in a region of northern
Minnesota showed the average age to be x = 2.03 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...

A random sample of 51 adult coyotes in a region of northern
Minnesota showed the average age to be x = 2.03 years, with sample
standard deviation s = 0.80 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...

A random sample of 41 adult coyotes in a region of northern
Minnesota showed the average age to be x = 2.05 years,
with sample standard deviation s = 0.78 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...

A random sample of 41 adult coyotes in a region of northern
Minnesota showed the average age to be x = 2.09 years, with sample
standard deviation s = 0.88 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...

A random sample of 46 adult coyotes in a region of northern
Minnesota showed the average age to be x = 2.05 years, with sample
standard deviation s = 0.84 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...

The price to earnings ratio (P/E) is an important tool in
financial work. A random sample of 14 large U.S. banks (J. P.
Morgan, Bank of America, and others) gave the following P/E
ratios.†
24
16
22
14
12
13
17
22
15
19
23
13
11
18
The sample mean is
x ≈ 17.1.
Generally speaking, a low P/E ratio indicates a "value" or
bargain stock. Suppose a recent copy of a magazine indicated that
the P/E ratio of...

A random sample of 36 values is drawn from a mound-shaped and
symmetric distribution. The sample mean is 14 and the sample
standard deviation is 2. Use a level of significance of 0.05 to
conduct a two-tailed test of the claim that the population mean is
13.5.
(a) Is it appropriate to use a Student's t
distribution? Explain.
Yes, because the x distribution is mound-shaped and
symmetric and σ is unknown.No, the x distribution
is skewed left. No, the x
distribution...

A random sample of 16 values is drawn from a mound-shaped and
symmetric distribution. The sample mean is 11 and the sample
standard deviation is 2. Use a level of significance of 0.05 to
conduct a two-tailed test of the claim that the population mean is
10.5.
(a) Is it appropriate to use a Student's t
distribution? Explain.
Yes, because the x distribution is mound-shaped and
symmetric and σ is unknown.No, the x distribution
is skewed left. No, the x
distribution...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 36 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago