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What is a critical value for a 2 sided z-test with a significance level of 10%? 1.65 2.33 2.58 1.28 186,282.3545

What is a critical value for a 2 sided z-test with a significance level of 10%? 1.65 2.33 2.58 1.28 186,282.3545

MATLAB: An Introduction with Applications
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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### Understanding Critical Values in a Z-Test When conducting a two-sided z-test in statistics, it's essential to determine the critical value that corresponds to your chosen significance level. The significance level, often denoted by alpha (α), measures the probability of rejecting the null hypothesis when it is actually true (Type I error). In this instance, we are dealing with a significance level of 10%, or 0.10. For a two-sided test, this significance level is split between the two tails of the standard normal distribution, so each tail has an area of 0.05 (5%). #### Question: **What is a critical value for a 2-sided z-test with a significance level of 10%?** #### Options: 1. 1.65 2. 2.33 3. 2.58 4. 1.28 5. 186,282.3545 #### Explanation: - **Option 1 (1.65)**: This is not the correct value for a 10% significance level for a two-sided z-test. - **Option 2 (2.33)**: This value usually corresponds to a much lower significance level (closer to 1%). - **Option 3 (2.58)**: This value also represents a much lower significance level (around 1%). - **Option 4 (1.28)**: This value is not a standard critical value for common alpha levels. - **Option 5 (186,282.3545)**: This is not a realistic z-value for any standard statistical calculation. #### Correct Answer: The correct critical value for a two-sided z-test with a significance level of 10% (α = 0.10) is **1.65**. This means that if your z-test statistic falls beyond ±1.65, you would reject the null hypothesis at the 10% significance level. #### Diagram: [If there were any diagrams or graphs in the image, you would describe them here in detail.] Understanding these values helps in making informed decisions in hypothesis testing, ensuring that the conclusions drawn from statistical analyses are robust and meaningful. For further practice, one can refer to z-tables or use statistical software to verify and understand the critical values for different significance levels.
Transcribed Image Text:### Understanding Critical Values in a Z-Test When conducting a two-sided z-test in statistics, it's essential to determine the critical value that corresponds to your chosen significance level. The significance level, often denoted by alpha (α), measures the probability of rejecting the null hypothesis when it is actually true (Type I error). In this instance, we are dealing with a significance level of 10%, or 0.10. For a two-sided test, this significance level is split between the two tails of the standard normal distribution, so each tail has an area of 0.05 (5%). #### Question: **What is a critical value for a 2-sided z-test with a significance level of 10%?** #### Options: 1. 1.65 2. 2.33 3. 2.58 4. 1.28 5. 186,282.3545 #### Explanation: - **Option 1 (1.65)**: This is not the correct value for a 10% significance level for a two-sided z-test. - **Option 2 (2.33)**: This value usually corresponds to a much lower significance level (closer to 1%). - **Option 3 (2.58)**: This value also represents a much lower significance level (around 1%). - **Option 4 (1.28)**: This value is not a standard critical value for common alpha levels. - **Option 5 (186,282.3545)**: This is not a realistic z-value for any standard statistical calculation. #### Correct Answer: The correct critical value for a two-sided z-test with a significance level of 10% (α = 0.10) is **1.65**. This means that if your z-test statistic falls beyond ±1.65, you would reject the null hypothesis at the 10% significance level. #### Diagram: [If there were any diagrams or graphs in the image, you would describe them here in detail.] Understanding these values helps in making informed decisions in hypothesis testing, ensuring that the conclusions drawn from statistical analyses are robust and meaningful. For further practice, one can refer to z-tables or use statistical software to verify and understand the critical values for different significance levels.
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