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 22 transects gave a sample variance s² = 51.5 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.

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

lower limit
upper limit

Answer 1

using excel>Addin>phstat>confidence intrval

we have

Confidence Interval Estimate for the Population Variance
Data
Sample Size	22
Sample Standard Deviation	7.17635
Confidence Level	95%
Intermediate Calculations
Degrees of Freedom	21
Sum of Squares	1081.5
Single Tail Area	0.025
Lower Chi-Square Value	10.2829
Upper Chi-Square Value	35.47888
Results
Interval Lower Limit for Variance	30.48293
Interval Upper Limit for Variance	105.1746
Interval Lower Limit for Standard Deviation	5.521135
Interval Upper Limit for Standard Deviation	10.25547

the requested confidence interval for the population variance.

lower limit = 30.48

upper limit = 105.18