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3. If I have a hypothesis test with critical values of 1.96 and -1.96 and I get a test statistic of my sample mean of 1.97 do I accept or reject my null hypothesis. What else should I infer about acceptance or rejection of the null hypothesis?

3. If I have a hypothesis test with critical values of 1.96 and -1.96 and I get a test statistic of my sample mean of 1.97 do I accept or reject my null hypothesis. What else should I infer about acceptance or rejection of the null hypothesis?

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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### Null Hypothesis Decision Making **Question:** 3. If I have a hypothesis test with critical values of 1.96 and -1.96 and I get a test statistic of my sample mean of 1.97, do I accept or reject my null hypothesis? What else should I infer about acceptance or rejection of the null hypothesis? **Discussion:** In hypothesis testing, you determine whether to accept or reject the null hypothesis (H0) based on comparison between your test statistic and critical values. Here are the general steps to follow: 1. **Identify Critical Values:** - Critical values are the thresholds that separate the acceptance region from the rejection region. - In this case, the critical values are 1.96 and -1.96. 2. **Evaluate Test Statistic:** - Compare your test statistic (1.97) with the critical values. - If the test statistic falls outside the range of critical values (-1.96 to 1.96), the null hypothesis can be rejected. 3. **Decision:** - Since 1.97 is greater than 1.96, the test statistic falls in the rejection region. - Thus, the null hypothesis should be rejected. 4. **Additional Inference:** - Rejecting the null hypothesis indicates that there is significant evidence to support the alternative hypothesis, suggesting that the observed effect is statistically significant. By following this approach, you'll be able to make informed decisions about hypothesis testing and infer the significance of your findings effectively.
Transcribed Image Text:### Null Hypothesis Decision Making **Question:** 3. If I have a hypothesis test with critical values of 1.96 and -1.96 and I get a test statistic of my sample mean of 1.97, do I accept or reject my null hypothesis? What else should I infer about acceptance or rejection of the null hypothesis? **Discussion:** In hypothesis testing, you determine whether to accept or reject the null hypothesis (H0) based on comparison between your test statistic and critical values. Here are the general steps to follow: 1. **Identify Critical Values:** - Critical values are the thresholds that separate the acceptance region from the rejection region. - In this case, the critical values are 1.96 and -1.96. 2. **Evaluate Test Statistic:** - Compare your test statistic (1.97) with the critical values. - If the test statistic falls outside the range of critical values (-1.96 to 1.96), the null hypothesis can be rejected. 3. **Decision:** - Since 1.97 is greater than 1.96, the test statistic falls in the rejection region. - Thus, the null hypothesis should be rejected. 4. **Additional Inference:** - Rejecting the null hypothesis indicates that there is significant evidence to support the alternative hypothesis, suggesting that the observed effect is statistically significant. By following this approach, you'll be able to make informed decisions about hypothesis testing and infer the significance of your findings effectively.
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