# 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 19 transects gave a sample variance s2 = 49.3 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.(a) What is the level of significance?State the null and alternate hypotheses.Ho: σ2 = 42.3; H1: σ2 > 42.3Ho: σ2 > 42.3; H1: σ2 = 42.3    Ho: σ2 = 42.3; H1: σ2 < 42.3Ho: σ2 = 42.3; H1: σ2 ≠ 42.3(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)What are the degrees of freedom?What assumptions are you making about the original distribution?We assume a exponential population distribution.We assume a uniform population distribution.    We assume a binomial population distribution.We assume a normal population distribution.(c) Find or estimate the P-value of the sample test statistic.P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.(e) Interpret your conclusion in the context of the application.At the 5% level of significance, there is insufficient evidence to conclude conclude that the variance is greater in the new section.At the 5% level of significance, there is sufficient evidence to conclude conclude that the variance is greater in the new section.    (f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)lower limit upper limit     Interpret the results in the context of the application.We are 95% confident that σ2 lies above this interval.We are 95% confident that σ2 lies within this interval.    We are 95% confident that σ2 lies below this interval.We are 95% confident that σ2 lies outside this interval.

Question
151 views

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 19 transects gave a sample variance s2 = 49.3 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.

(a) What is the level of significance?

State the null and alternate hypotheses.
Ho: σ2 = 42.3; H1: σ2 > 42.3Ho: σ2 > 42.3; H1: σ2 = 42.3    Ho: σ2 = 42.3; H1: σ2 < 42.3Ho: σ2 = 42.3; H1: σ2 ≠ 42.3

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

What are the degrees of freedom?

What assumptions are you making about the original distribution?
We assume a exponential population distribution.We assume a uniform population distribution.    We assume a binomial population distribution.We assume a normal population distribution.

(c) Find or estimate the P-value of the sample test statistic.
P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.
At the 5% level of significance, there is insufficient evidence to conclude conclude that the variance is greater in the new section.At the 5% level of significance, there is sufficient evidence to conclude conclude that the variance is greater in the new section.

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

Interpret the results in the context of the application.
We are 95% confident that σ2 lies above this interval.We are 95% confident that σ2 lies within this interval.    We are 95% confident that σ2 lies below this interval.We are 95% confident that σ2 lies outside this interval.
check_circle

Step 1

Note:Hey there! Thank you for posting the question. However, since your question has more than 3sub parts, according to our policy, we have solved the first 3 sub parts for you. If you need help with any other part, please re-post the question and mention the part you need help with.

Step 2

It is given that the population variance is 42.3 and the sample variance is 49.3. The significance level is 0.05 and the sample size is 19.

Step 3

a).

The level of significance is 0.05.

The null and al...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in