The following problem is based on information from Archaeological Surveys of Chaco Canyon, New Mexico, by A. Hayes, D. Brugge, and W. Judge, University of New Mexico Press. 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 s² = 42.3. In a different section of Chaco Canyon, a random sample of 23 transects gave a sample variance s² = 46.1 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.

Please provide the following information.

(a) What is the level of signi­ficance? State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. 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.

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

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

(f) Find the requested confi­dence interval for the population variance or population standard deviation. Interpret the results in the context of the application.