Question

A transect is an archaeological study area that is  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 . In a different section of Chaco Canyon, a random sample of 23 transects gave a sample variance  for the number of sites per transect. Use an  to test the claim that the variance in the new section is greater than 35.0. Find a 95% confidence interval for the population variance.

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Find the requested confidence interval for the population variance. Interpret the results in the context of the application.

Choose the best one.

22.87 to 76.50

20.96 to 70.13

30.92 to 103.59

21.92 to 73.32

32.37 to 108.30

Answer 1

ANSWER::

Please check your question values are missing......i hope this will helpfull to you

given data are:-

sample variance (s2) = 51.7

sample size (n) = 23

a).

Hypothesis :-

[ claim ]

the test statistic be:-

degrees of freedom = (n-1) = (23-1) = 22

p value is :-

[ in any blank cell of excel type =CHISQ.DIST.RT(32.497,22) ]

decision:-

p value = 0.0693 > 0.01 (alpha)

we fail to reject the null hypothesis and conclude that there is not enough evidence to claim that the variance in the new section is greater than 35.0

b).

chi square critical values for df=22, alpha=0.05 , both tailed test be:-

	critical values	excel function
	10.982	=CHISQ.INV.RT(0.975,22)
	36.781	=CHISQ.INV.RT(0.025,22)

the 95% confidence interval for the population variance be:-

[ this is the nearest among the options provided ]

interpretation:-

we are 95% confident that the true population variance will be within 30.92 and 103.59

Option:: (C) is correct...............

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