### 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