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 28 transects gave a sample variance s2 = 48.3 for the number of sites per transect. Required:
Use a 5% level of significance to test the claim that the variance in the new section is greater than 42.3.

There is significant evidence to conclude that carina e in New section is greater than 42.3

Step-by-step explanation:

Given :

Sample variance, s² = 48.3

Population variance, σ² = 42.3

Sample size, n = 28

α = 0.05

The hypothesis :

H0 : σ² = 42.3

H0 : σ² > 42.3

The test statistic, χ² : (n-1)*s²/σ²

χ² = [(28 - 1) * 48.3] / 42.3

χ² = (27 * 48.3) / 42.3

χ² = 1304.1 / 42.3

χ² = 30.829787

χ² = 30.830

The Critical value at α = 0.05 ; df = (28-1) = 27

Critical value(0.05, 27) = 27.587

Reject H0 if χ² statistic > Critical value

Since, 30.830 > 27.587 ; Reject H0 ; and conclude that variance in the new section is greater than 42.3

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: