A transect is an archaeological study area that is 1/5mile wide and 1 mile long. A site in a transect is thelocation of a significant archaeological find. Let xrepresent the number of sites per transect. In a section of ChacoCanyon, a large number of transects showed that x has apopulation variance σ² = 42.3. In a differentsection of Chaco Canyon, a random sample of 26 transects gave asample variance s² = 46.7 for the number ofsites per transect. Use a 5% level of significance to test theclaim 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: σ² = 42.3;H₁: σ² < 42.3

H_o: σ² = 42.3;H₁: σ² >42.3  

  H_o: σ² >42.3; H₁: σ² = 42.3

H_o: σ² = 42.3;H₁: σ² ≠ 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 originaldistribution?

We assume a uniform population distribution.

We assume a binomial populationdistribution.    

We assume a normal population distribution.

We assume a exponential population distribution.

(c) Find or estimate the P-value of the sample teststatistic.

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 orfail to reject the null hypothesis?

Since the P-value > α, we fail to rejectthe null hypothesis.

Since the P-value > α, we reject the nullhypothesis.    

Since the P-value ≤ α, we reject the nullhypothesis.

Since the P-value ≤ α, we fail to reject thenull hypothesis.

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

At the 5% level of significance, there is insufficient evidenceto conclude conclude that the variance is greater in the newsection.At the 5% level of significance, there is sufficientevidence to conclude conclude that the variance is greater in thenew section.    

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

lower limit
upper limit   Â

Interpret the results in the context of the application.

We are 95% confident that σ² lies below thisinterval.

We are 95% confident that σ² lies outsidethis interval.   

We are 95% confident that σ² lies withinthis interval.

We are 95% confident that σ² lies above thisinterval.