Question

Asked Nov 25, 2019

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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 19 transects gave a sample variance *s*^{2} = 49.3 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}: σ^{2} = 42.3; *H*_{1}: σ^{2} > 42.3*H*_{o}: σ^{2} > 42.3; *H*_{1}: σ^{2} = 42.3 *H*_{o}: σ^{2} = 42.3; *H*_{1}: σ^{2} < 42.3*H*_{o}: σ^{2} = 42.3; *H*_{1}: σ^{2} ≠ 42.3

(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?

(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?

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

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

Interpret the results in the context of the application.

State the null and alternate hypotheses.

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

(c) Find or estimate the

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

Step 1

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Step 2

It is given that the population variance is 42.3 and the sample variance is 49.3. The significance level is 0.05 and the sample size is 19.

Step 3

a).

The level of significance is 0.05.

The null and al...

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