Test the claim that the population variance of percentage yields on assets for South Korean companies is higher than that for companies in Sweden. Use a 5% level of significance. How could your test conclusion relate to an economist's question regarding volatility of corporate productivity of large companies in South Korea compared with those in Sweden? (a) What is the level of significance? State the null and alternate hypotheses. Ho: ?12 = ?22; H1: ?12 > ?22Ho: ?12 > ?22; H1: ?12 = ?22 Ho: ?22 = ?12; H1: ?22 > ?12Ho: ?12 = ?22; H1: ?12 ≠ ?22 (b) Find the value of the sample F statistic. (Use 2 decimal places.) What are the degrees of freedom? dfN dfD What assumptions are you making about the original distribution? The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent chi-square distributions. We have random samples from each population. The populations follow independent normal distributions. We have random samples from each population.The populations follow independent normal distributions. (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 < 0.0250.001 < p-value < 0.010p-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies.Reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies. Reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies.Fail to reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies.

Test the claim that the population variance of percentage yields on assets for South Korean companies is higher than that for companies in Sweden. Use a 5% level of significance. How could your test conclusion relate to an economist's question regarding volatility of corporate productivity of large companies in South Korea compared with those in Sweden? (a) What is the level of significance? State the null and alternate hypotheses. Ho: ?12 = ?22; H1: ?12 > ?22Ho: ?12 > ?22; H1: ?12 = ?22 Ho: ?22 = ?12; H1: ?22 > ?12Ho: ?12 = ?22; H1: ?12 ≠ ?22 (b) Find the value of the sample F statistic. (Use 2 decimal places.) What are the degrees of freedom? dfN dfD What assumptions are you making about the original distribution? The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent chi-square distributions. We have random samples from each population. The populations follow independent normal distributions. We have random samples from each population.The populations follow independent normal distributions. (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 < 0.0250.001 < p-value < 0.010p-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies.Reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies. Reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies.Fail to reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies.

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 random sample of leading companies in South Korea gave the following percentage yields based on assets.

2.3	2.2	4.1	1.5	0.9	3.6	2.4
0.2	1.7	1.8	1.4	5.4	1.1

Use a calculator to verify that s² ≈ 2.025 for these South Korean companies.

Another random sample of leading companies in Sweden gave the following percentage yields based on assets.

2.4

3.7

1.6

3.7

2.8

2.3

3.5

2.8

Use a calculator to verify that s² ≈ 0.573 for these Swedish companies.

Test the claim that the population variance of percentage yields on assets for South Korean companies is higher than that for companies in Sweden. Use a 5% level of significance. How could your test conclusion relate to an economist's question regarding volatility of corporate productivity of large companies in South Korea compared with those in Sweden?

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: ?₁² = ?₂²; H₁: ?₁² > ?₂²H_o: ?₁² > ?₂²; H₁: ?₁² = ?₂² H_o: ?₂² = ?₁²; H₁: ?₂² > ?₁²H_o: ?₁² = ?₂²; H₁: ?₁² ≠ ?₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)

What are the degrees of freedom?

df_N
df_D

What assumptions are you making about the original distribution?

The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent chi-square distributions. We have random samples from each population. The populations follow independent normal distributions. We have random samples from each population.The populations follow independent normal distributions.

p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.001 < p-value < 0.010p-value < 0.001

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

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies.Reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies. Reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies.Fail to reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is greater in the South Korean companies.

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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