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.

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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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.

H_o: σ² = 42.3; H₁: σ² > 42.3H_o: σ² > 42.3; H₁: σ² = 42.3 H_o: σ² = 42.3; H₁: σ² < 42.3H_o: 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.

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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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