Question

A *transect* is an archaeological study area that is 1/5
mile wide and 1 mile long. A *site* in a transect is the
location of a significant archaeological find. Let *x*
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that *x* has a
population variance *σ*^{2} = 42.3. In a different
section of Chaco Canyon, a random sample of 24 transects gave a
sample variance *s*^{2} = 45.1 for the number of
sites per transect. Use a 5% level of significance to test the
claim that the variance in the new section is greater than 42.3.
Find a 95% confidence interval for the population variance.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H _{o}*:

(b) Find the value of the chi-square statistic for the sample.
(Round your answer to two decimal places.)

What are the degrees of freedom?

What assumptions are you making about the original
distribution?

We assume a binomial population distribution.We assume a exponential population distribution. We assume a normal population distribution.We assume a uniform population distribution.

(c) Find or 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?

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, there is insufficient evidence to conclude conclude that the variance is greater in the new section.At the 5% level of significance, there is sufficient evidence to conclude conclude that the variance is greater in the new section.

(f) Find the requested confidence interval for the population
variance. (Round your answers to two decimal places.)

lower limit | |

upper limit |

Interpret the results in the context of the application.

We are 95% confident that *σ*^{2} lies within
this interval.We are 95% confident that *σ*^{2} lies
outside this interval. We are 95% confident
that *σ*^{2} lies below this interval.We are 95%
confident that *σ*^{2} lies above this interval.

Answer #1

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

Hypotheses: *H _{o}*:

b) Test statistic = 24.52

Degrees of freedom = 23

We assume a normal population distribution.

c) *P*-value > 0.100

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

e) At the 5% level of significance, there is insufficient evidence to conclude conclude that the variance is greater in the new section.

f) 95% confidence interval:

Lower limit = 27.24

Upper limit = 88.74

We are 95% confident that *σ*^{2} lies within
this interval.

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 25 transects gave a
sample variance s2 = 47.9 for...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 26 transects gave a
sample variance s2 = 47.5 for...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 24 transects gave a
sample variance s2 = 50.7 for...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 18 transects gave a
sample variance s2 = 47.9 for...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 25 transects gave a
sample variance s2 = 47.3 for...

A transect is an archaeological study area that is 1/5 mile wide
and 1 mile long. A site in a transect is the location of a
significant archaeological find. Let x represent the number of
sites per transect. In a section of Chaco Canyon, a large number of
transects showed that x has a population variance σ2 = 42.3. In a
different section of Chaco Canyon, a random sample of 26 transects
gave a sample variance s2 = 50.1 for...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 27 transects gave a
sample variance s2 = 49.7 for...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 25 transects gave a
sample variance s2 = 45.7 for...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 24 transects gave a
sample variance s2 = 49.7 for...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 22 transects gave a
sample variance s2 = 51.5 for...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 17 minutes ago

asked 17 minutes ago

asked 29 minutes ago

asked 49 minutes 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 3 hours ago

asked 3 hours ago