### Analysis of Variance in Corporate ProductivityA random sample of leading companies in South Korea provided the following percentage yields based on assets:- 2.7, 1.7, 4.4, 1.1, 0.1, 3.6, 2.4- 0.2, 1.7, 1.8, 1.4, 5.4, 1.1Using a calculator, the variance \( s^2 \approx 2.449 \) for these South Korean companies.Another sample from leading companies in Sweden provided these yields:- 2.1, 3.3, 3.1, 1.6, 3.4, 2.8, 2.3, 3.5, 2.8The variance is \( s^2 \approx 0.420 \) for these Swedish companies.#### Hypothesis TestingTo test if the population variance of percentage yields for South Korean companies is higher than that for Swedish companies, we use a 5% level of significance. This relates to understanding volatility in corporate productivity between South Korea and Sweden.**(a) What is the level of significance?***Answer:* 5%**State the null and alternate hypotheses:**- \( H_0: \sigma_1^2 = \sigma_2^2 \)- \( H_i: \sigma_1^2 > \sigma_2^2 \)**(b) Calculate the Sample F Statistic:**Find the value of the sample F statistic using two decimal places. This involves the formula for comparing two variances:\[ F = \frac{\text{Variance of South Korean companies}}{\text{Variance of Swedish companies}} \approx \frac{2.449}{0.420} \]**Degrees of Freedom:**- \( df_N \) (numerator): Sample size minus one for South Korean companies.- \( df_D \) (denominator): Sample size minus one for Swedish companies.**What assumptions are made about the original distributions?**Option: The populations follow independent normal distributions. We have random samples from each population.**(c) Find the P-value for the sample test statistic.**Compute this using the F-distribution tables or statistical software.### ConclusionThis test helps determine if there is a statistically significant difference in variance between the **Math 2250 Unit 4 Post Test Review**(b) Find the value of the sample F statistic. (Use 2 decimal places.)\[ \text{F statistic: } \_\_\_\_\_\_\_\_\_\_ \]**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.**(c) Find or estimate the \( P \)-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- ☐ 0.001 < \( P \)-value < 0.010- ☐ \( P \)-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 \( \alpha = 0.05 \) level, we reject the null hypothesis and conclude the data is not statistically significant.- ☐ At the \( \alpha = 0.05 \) level, we reject the null hypothesis and conclude the data is statistically significant.- ☐ At the \( \alpha = 0.05 \) level, we fail to reject the null hypothesis and conclude the data are not statistically significant.- ☐ At the \( \alpha = 0.05 \) 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

Name: ### Analysis of Variance in Corporate ProductivityA random sample of
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Description: ### Analysis of Variance in Corporate ProductivityA random sample of leading companies in South Korea provided the following percentage yields based on assets:- 2.7, 1.7, 4.4, 1.1, 0.1, 3.6, 2.4- 0.2, 1.7, 1.8, 1.4, 5.4, 1.1Using a calculator, the v