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 20 transects gave a sample variance s2 = 45.1 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 99% confidence interval for the population variance.

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

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 p transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance of = 42.3. In a different section of Chaco Canyon, a random sample of 20 tra gave a sample variance s2-45.1 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 9 confidence interval for the population variance (a) What is the level of significance? 10 State the null and alternate hypotheses O Ho: 2 = 42.3; H1:02 * 42.3 Hai 2 = 42.3; H1: 2 > 42.3 O Ho: 2 > 42.3; H1: 2 = 42.3 (b) Find the value of the chi-square statistic for the sample. (Use 2 decimal places.) 20.26 What are the degrees of freedom? 19 What assumptions are you making about the original distribution? we assume a normal population distribution. o We assume a binomial population distribution. o We assume a uniform population distribution. o We assume a exponential population distribution. (c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.) 27.2 (d) Rased on your answers in narts (a) to (c), will you reiect or fail to reject the null hynothesis?

Explanation / Answer

The statistical software output for this problem is:

One sample variance hypothesis test:
2 : Variance of population
H0 : 2 = 42.3
HA : 2 > 42.3

Hypothesis test results:

Hence,

P - value = 0.3792

We do not reject the null hypothesis.

Variance Sample Var. DF Chi-square Stat P-value 2 45.1 19 20.257683 0.3792

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