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### Critical Z-Value in Hypothesis Testing When conducting a hypothesis test, determining the critical value is a crucial step to decide whether or not to reject the null hypothesis. **Given Problem:** - Assume that the data has a normal distribution. - The number of observations is greater than fifty. - Find the critical Z value used to test a null hypothesis for α = 0.05 for a two-tailed test. **Solution:** 1. **Understanding Two-Tailed Test:** - In a two-tailed test, the area under the standard normal distribution curve is split between the two tails. - Since α = 0.05, each tail will contain 0.025 (since 0.05 / 2 = 0.025) of the data. 2. **Finding the Critical Z-Values:** - You will need to find the Z-values that correspond to the cumulative probabilities of 0.025 and 0.975 (because 1 - 0.025 = 0.975). - Using a standard normal distribution table or a statistical tool, you find: - The Z-value for 0.025 is approximately -1.96. - The Z-value for 0.975 is approximately 1.96. **Conclusion:** The critical Z-values for a two-tailed test with α = 0.05 are -1.96 and 1.96. If the calculated Z-value of your test statistic falls beyond these critical values, you would reject the null hypothesis. **Notes for Students:** - Ensure to always split the significance level α by 2 when dealing with a two-tailed test. - Utilize standard normal distribution tables or computational tools for accurate Z-values. - Correct interpretation of these critical values is essential for hypothesis testing and making accurate statistical inferences.

### Critical Z-Value in Hypothesis Testing When conducting a hypothesis test, determining the critical value is a crucial step to decide whether or not to reject the null hypothesis. **Given Problem:** - Assume that the data has a normal distribution. - The number of observations is greater than fifty. - Find the critical Z value used to test a null hypothesis for α = 0.05 for a two-tailed test. **Solution:** 1. **Understanding Two-Tailed Test:** - In a two-tailed test, the area under the standard normal distribution curve is split between the two tails. - Since α = 0.05, each tail will contain 0.025 (since 0.05 / 2 = 0.025) of the data. 2. **Finding the Critical Z-Values:** - You will need to find the Z-values that correspond to the cumulative probabilities of 0.025 and 0.975 (because 1 - 0.025 = 0.975). - Using a standard normal distribution table or a statistical tool, you find: - The Z-value for 0.025 is approximately -1.96. - The Z-value for 0.975 is approximately 1.96. **Conclusion:** The critical Z-values for a two-tailed test with α = 0.05 are -1.96 and 1.96. If the calculated Z-value of your test statistic falls beyond these critical values, you would reject the null hypothesis. **Notes for Students:** - Ensure to always split the significance level α by 2 when dealing with a two-tailed test. - Utilize standard normal distribution tables or computational tools for accurate Z-values. - Correct interpretation of these critical values is essential for hypothesis testing and making accurate statistical inferences.

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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### Critical Z-Value in Hypothesis Testing When conducting a hypothesis test, determining the critical value is a crucial step to decide whether or not to reject the null hypothesis. **Given Problem:** - Assume that the data has a normal distribution. - The number of observations is greater than fifty. - Find the critical Z value used to test a null hypothesis for α = 0.05 for a two-tailed test. **Solution:** 1. **Understanding Two-Tailed Test:** - In a two-tailed test, the area under the standard normal distribution curve is split between the two tails. - Since α = 0.05, each tail will contain 0.025 (since 0.05 / 2 = 0.025) of the data. 2. **Finding the Critical Z-Values:** - You will need to find the Z-values that correspond to the cumulative probabilities of 0.025 and 0.975 (because 1 - 0.025 = 0.975). - Using a standard normal distribution table or a statistical tool, you find: - The Z-value for 0.025 is approximately -1.96. - The Z-value for 0.975 is approximately 1.96. **Conclusion:** The critical Z-values for a two-tailed test with α = 0.05 are -1.96 and 1.96. If the calculated Z-value of your test statistic falls beyond these critical values, you would reject the null hypothesis. **Notes for Students:** - Ensure to always split the significance level α by 2 when dealing with a two-tailed test. - Utilize standard normal distribution tables or computational tools for accurate Z-values. - Correct interpretation of these critical values is essential for hypothesis testing and making accurate statistical inferences.
Transcribed Image Text:### Critical Z-Value in Hypothesis Testing When conducting a hypothesis test, determining the critical value is a crucial step to decide whether or not to reject the null hypothesis. **Given Problem:** - Assume that the data has a normal distribution. - The number of observations is greater than fifty. - Find the critical Z value used to test a null hypothesis for α = 0.05 for a two-tailed test. **Solution:** 1. **Understanding Two-Tailed Test:** - In a two-tailed test, the area under the standard normal distribution curve is split between the two tails. - Since α = 0.05, each tail will contain 0.025 (since 0.05 / 2 = 0.025) of the data. 2. **Finding the Critical Z-Values:** - You will need to find the Z-values that correspond to the cumulative probabilities of 0.025 and 0.975 (because 1 - 0.025 = 0.975). - Using a standard normal distribution table or a statistical tool, you find: - The Z-value for 0.025 is approximately -1.96. - The Z-value for 0.975 is approximately 1.96. **Conclusion:** The critical Z-values for a two-tailed test with α = 0.05 are -1.96 and 1.96. If the calculated Z-value of your test statistic falls beyond these critical values, you would reject the null hypothesis. **Notes for Students:** - Ensure to always split the significance level α by 2 when dealing with a two-tailed test. - Utilize standard normal distribution tables or computational tools for accurate Z-values. - Correct interpretation of these critical values is essential for hypothesis testing and making accurate statistical inferences.
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