Atransectis an archaeological study area that is 1/5 mile wide and 1 mile long. Asitein a transect is the location of a significant archaeological find. Letxrepresent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed thatxhas a population variance²= 42.3. In a different section of Chaco Canyon, a random sample of21transects gave a sample variances²=50.9for 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:²= 42.3;H₁:²> 42.3

H_o:²= 42.3;H₁:²42.3

H_o:²= 42.3;H₁:²< 42.3

H_o:²> 42.3;H₁:²= 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?

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 theP-value of the sample test statistic.

P-value > 0.100

0.050 <P-value < 0.100

0.025 <P-value < 0.050

0.010 <P-value < 0.025

0.005 <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 theP-value >, we fail to reject the null hypothesis.

Since theP-value >, we reject the null hypothesis.

Since theP-value, we reject the null hypothesis.

Since theP-value, 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 limitupper limit

Interpret the results in the context of the application.

We are 95% confident that²lies below this interval.

We are 95% confident that²lies within this interval.

We are 95% confident that²lies outside this interval.

We are 95% confident that²lies above this interval.