A transect is an archaeological study area that is 1/5 mile wide and 1 mile long

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 2 = 42.3. In a different section of Chaco Canyon, a random sample of 21 transects gave a sample variance s2 = 46.3 for the number of sites per transect. Use a 10% level of significance to test the claim that the variance in the new section is greater than 42.3. Find a 90% confidence interval for the population variance.

(a) What is the level of significance?

(b) Find the value of the chi-square statistic for the sample. (Use 2 decimal places.)

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

(f) Find the requested confidence interval for the population variance or population standard deviation. (Use 2 decimal places.)

Explanation / Answer

a) Level of significance:0.10

b) T=(n-1)(s/sigma)^2

=(21-1)(46.3/42.3)

=21.89

df=n-1=20

c) p value is:0.3465

d) (n-1)s^2/X^220,0.10/2,(n-1)s^2/X?^220,1-0.10/2

=20*46.3/30.144,20*46.3/10.117

=30.72, 91.53

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