**Hypothesis Testing with Different Critical Values: An Educational Insight****Introduction:**In statistical hypothesis testing, selecting the appropriate critical values is crucial for accurate decision-making. This example illustrates the impact of choosing different critical values in a two-tailed hypothesis test.**Scenario Explanation:**For a two-tailed hypothesis test with a certain data set, we have two different approaches for determining degrees of freedom (df):1. **Using a conservative approach:** - Degrees of freedom calculated as the smaller of \( n_1 - 1 \) and \( n_2 - 1 \), resulting in \( df = 11 \). - Corresponding critical values: \( t = \pm 2.201 \).2. **Using the formula for exact degrees of freedom:** - Results in \( df = 19.063 \). - Corresponding critical values: \( t = \pm 2.093 \).**Task:**Determine why using the critical values of \( t = \pm 2.201 \) is more "conservative" compared to the critical values of \( \pm 2.093 \).**Options:**Choose the correct answer from the following:**A.** Using the critical values of \( t = \pm 2.201 \) is less likely to lead to rejection of the null hypothesis than using the critical values of \( \pm 2.093 \).**B.** Using the critical values of \( t = \pm 2.201 \) is more likely to lead to rejection of the null hypothesis than using the critical values of \( \pm 2.093 \).**C.** Using the critical values of \( t = \pm 2.201 \) results in rounding the test statistic to more decimal places than using the critical values of \( \pm 2.093 \).**D.** Using the critical values of \( \pm 2.201 \) requires fewer calculations than using the critical values of \( \pm 2.093 \).**Analysis:**Choosing a more conservative critical value (higher in absolute terms) like \( \pm 2.201 \) generally results in a lower likelihood of rejecting the null hypothesis, favoring the maintenance of the null until there is strong enough evidence against it. This approach reduces the risk of a Type I error, aligning with a more cautious stance in hypothesis testing.**Conclusion:**Understanding

Name: **Hypothesis Testing with Different Critical Values: An Educational I
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Description: **Hypothesis Testing with Different Critical Values: An Educational Insight****Introduction:**In statistical hypothesis testing, selecting the appropriate critical values is crucial for accurate decision-making. This example illustrates the impact o

When the critical value is increased, the rejection region for the null hypothesis is decreased,…

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Statistics

For conducting a two-tailed hypothesis test with a certain data set, using the smaller of n,-1 and ng-1 for the degrees of freedom results in df = 11, and the coresponding critical values are t 12201. Using the formula for the exact degrees of freedom results in df= 19.063, and the corresponding critical values are t+2.093. How is using the critical values of t=+2.201 more "conservative" than using the critical values of +2.093? Choose the correct answer below. O A. Using the critical values of t= +2.201 is less likely to lead to rejection of the null hypothesis than using the critical values of 2.093 O B. Using the critical values of t= +2.201 is more likely to lead to rejection of the null hypothesis than using the critical values of 2.093. OC. Using the critical values of t= +2.201 results in rounding the test statistic to more decimal places than using the critical values of 2.093 OD. Using the critical values of t= 12.201 requires fewer calculations than using the critical values of t2.093.

For conducting a two-tailed hypothesis test with a certain data set, using the smaller of n,-1 and ng-1 for the degrees of freedom results in df = 11, and the coresponding critical values are t 12201. Using the formula for the exact degrees of freedom results in df= 19.063, and the corresponding critical values are t+2.093. How is using the critical values of t=+2.201 more "conservative" than using the critical values of +2.093? Choose the correct answer below. O A. Using the critical values of t= +2.201 is less likely to lead to rejection of the null hypothesis than using the critical values of 2.093 O B. Using the critical values of t= +2.201 is more likely to lead to rejection of the null hypothesis than using the critical values of 2.093. OC. Using the critical values of t= +2.201 results in rounding the test statistic to more decimal places than using the critical values of 2.093 OD. Using the critical values of t= 12.201 requires fewer calculations than using the critical values of t2.093.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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