Atransectis an archaeological study area that is 1/5 mile wide and 1 mile long. Asitein a transect is the location of a significant archaeological find. Letxrepresent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed thatxhas a population variance²= 42.3. In a different section of Chaco Canyon, a random sample of20transects gave a sample variances²=44.5for 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.

(a) What is the level of significance?

(b) State the null and alternate hypotheses.

• H₀:²= 42.3;H₁:²42.3
• H₀:²= 42.3;H₁:²< 42.3
• H₀:²> 42.3;H₁:²= 42.3
• H₀:²= 42.3;H₁:²> 42.3

(c) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

(d) What are the degrees of freedom?

(e) What assumptions are you making about the original distribution?

• We assume a binomial population distribution.
• We assume a exponential population distribution.
• We assume a uniform population distribution.
• We assume a normal population distribution.

(f) Find or estimate theP-value of the sample test statistic.

• P-value > 0.100
• 0.050 <P-value < 0.100
• 0.025 <P-value < 0.050
• 0.010 <P-value < 0.025
• 0.005 <P-value < 0.010
• P-value < 0.005

(g) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

• Since theP-value >, we fail to reject the null hypothesis.
• Since theP-value >, we reject the null hypothesis.
• Since theP-value, we reject the null hypothesis.
• Since theP-value, we fail to reject the null hypothesis.