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 σ² = 42.3. In a different section of Chaco Canyon, a random sample of 18 transects gave a sample variance s² = 51.1 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 the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

Find or estimate the P-value of the sample test statistic.

A-P-value > 0.100

B-0.050 < P-value < 0.100    

C-0.025 < P-value < 0.050

D-0.010 < P-value < 0.025

E-0.005 < P-value < 0.010

F-P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

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

B-Since the P-value > α, we reject the null hypothesis.    

C-Since the P-value ≤ α, we reject the null hypothesis.

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

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

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

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

Answer 1

An exact p-value in case of chi square is not required but it can be calculated using some online calculator-

I hope this helps you

Thanks