Question

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 σ² = 42.3. In a different section of Chaco Canyon, a random sample of 21 transects gave a sample variance s² = 47.7 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.

(A) What is the level of significance?

(B) State the null and alternate hypotheses

H₀: σ² = 42.3; H₁: σ² > 42.3

H₀: σ² = 42.3; H₁: σ² < 42.3    

H₀: σ² = 42.3; H₁: σ² ≠ 42.3

H₀: σ² < 42.3; H₁: σ² = 42.3

H₀: σ² > 42.3; H₁: σ² = 42.3

(C) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)

(D) What are the degrees of freedom?

(E) What assumptions are you making about the original distribution?

We assume a binomial population distribution.

We assume a normal population distribution.    

We assume a uniform population distribution.

We assume an exponential population distribution.

(F) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

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

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.

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

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

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

Answer 1

a) the level of significance is 5% that is 0.05

b) H0: σ^2 = 42.3; H1: σ^2 > 42.3

c) the value of the chi-square statistic for the sample

d) Degrees of freedom= 21-1=20

e) We assume a normal population distribution.

f) The P-Value is .311272. The result is not significant at p > .05.

g) Since the P-value > α, we fail to reject the null hypothesis

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