### Hypothesis Testing with Z-StatisticsIn hypothesis testing, the standardized test statistic \( z \) is used to determine whether to reject the null hypothesis. Here, we are given several \( z \) values to evaluate under the standard normal distribution curve.#### Given Values:- (a) \( z = 1.207 \)- (b) \( z = -1.323 \)- (c) \( z = -1.387 \)- (d) \( z = 1.195 \)#### Chart Explanation:The chart displays a standard normal distribution curve, showing areas under the curve which correspond to rejection and non-rejection regions for the null hypothesis. The critical \( z \)-value is marked at \( z_0 = -1.285 \), indicating the threshold beyond which we reject the null hypothesis.#### Question Analysis:(a) **For \( z = 1.207 \), should you reject or fail to reject the null hypothesis?**- **Options:** - A. Reject \( H_0 \) because \( z > -1.285 \). - B. Reject \( H_0 \) because \( z < -1.285 \). - C. Fail to reject \( H_0 \) because \( z < -1.285 \). - D. Fail to reject \( H_0 \) because \( z > -1.285 \).(b) **For \( z = -1.323 \), should you reject or fail to reject the null hypothesis?**- **Options:** - A. Fail to reject \( H_0 \) because \( z > -1.285 \). - B. Fail to reject \( H_0 \) because \( z < -1.285 \). - C. Reject \( H_0 \) because \( z < -1.285 \). - D. Reject \( H_0 \) because \( z > -1.285 \).To decide whether to reject or fail to reject \( H_0 \), compare the given \( z \)-values to the critical value \( z_0 = -1.285 \). If the value of \( z \) falls in the rejection region, the null hypothesis is rejected; otherwise, it is not. ### Hypothesis Testing with Z-ScoresConsider the following scenarios for hypothesis testing:#### (c) For \( z = -1.387 \), should you reject or fail to reject the null hypothesis?- **Option A**: Fail to reject \( H_0 \) because \( z > -1.285 \).- **Option B**: Fail to reject \( H_0 \) because \( z < -1.285 \).- **Option C**: Reject \( H_0 \) because \( z > -1.285 \).- **Option D**: Reject \( H_0 \) because \( z < -1.285 \).#### (d) For \( z = -1.195 \), should you reject or fail to reject the null hypothesis?- **Option A**: Reject \( H_0 \) because \( z > -1.285 \).- **Option B**: Fail to reject \( H_0 \) because \( z > -1.285 \).- **Option C**: Fail to reject \( H_0 \) because \( z < -1.285 \).- **Option D**: Reject \( H_0 \) because \( z < -1.285 \).### ExplanationIn hypothesis testing, we often compare the calculated z-score to a critical value to decide whether to reject the null hypothesis. The choice of rejection depends on whether the calculated z-value is more extreme than the critical value set for the test. If the z-value is more extreme (either more positive or more negative), the null hypothesis \( H_0 \) is rejected. Otherwise, we fail to reject it.

Here critical region is below -1.285 So use this to identify whether reject null hypothesis or not

Answered: ate whether the standardized test…

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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ate whether the standardized test statistic z indicates that you should reject the null hypothesis. (a) z= 1.207 (b) z = - 1.323 (c) z= - 1.387 (d) z= - 1.195