question 19 ### Educational Text on Statistical Testing and Analysis#### Z-Test CalculationThe image shows two calculator display screens related to a statistical Z-Test. Here's how each part of the process is detailed:**First Display:**- **Z-Test:** Shows `Input: Data` and `Stats`.- **ω (Population mean):** 742- **σ (Standard deviation):** 68.1- **x̄ (Sample mean):** 763- **n (Sample size):** 65- Test type: Two-tailed (μ ≠ ω)**Second Display:**- **ω (Population mean):** 742- **z (Z-score):** 2.486158777- **p (P-value):** 0.0064565285- **x̄ (Sample mean):** 763- **n (Sample size):** 65---#### Finding Critical Values and Rejection RegionsFor Exercises 19-24, determine the critical values and rejection regions for z-tests at various levels of significance (α). A graph should accompany your answer.19. **Left-tailed test, α = 0.03**20. **Left-tailed test, α = 0.09**21. **Right-tailed test, α = 0.05**22. **Right-tailed test, α = 0.08**23. **Two-tailed test, α = 0.02**24. **Two-tailed test, α = 0.12**---#### Graphical AnalysisFor Exercises 25 and 26, determine if the standardized test statistic $ z $ allows rejection of the null hypothesis. Provide reasoning for your decision.**Exercise 25:**- (a) $ z = -1.301 $- (b) $ z = 1.203 $- (c) $ z = 1.280 $- (d) $ z = 1.286 $**Exercise 26:**- (a) $ z = 1.98 $- (b) $ z = -1.89 $- (c) $ z = 1.65 $- (d) $ z = -1.99 $**Graph Explanation:**Two bell curve graphs are displayed:- **Graph for Exercise 25:** A standard normal distribution curve

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Description: question 19 ### Educational Text on Statistical Testing and Analysis#### Z-Test CalculationThe image shows two calculator display screens related to a statistical Z-Test. Here's how each part of the process is detailed:**First Display:**- **Z-Test:**

19. The test is left tailed, and the level of significance is 0.03. Computation of critical value: α=0.03 The critical value of z-distribution can be obtained using the excel formula “=NORM.S.INV(0.03)”. The critical value is -1.8808. Thus, the left-tailed critical value is -1.8808. Rejection region for left tailed: If the test statistic < critical value =-1.8808, then reject the null hypothesis H0.The graph is,

Answered: 19. Left-tailed test, a = α=0.03

Math

Statistics

19. Left-tailed test, a = α=0.03

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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Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.

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question 19

### Educational Text on Statistical Testing and Analysis

#### Z-Test Calculation
The image shows two calculator display screens related to a statistical Z-Test. Here's how each part of the process is detailed:

**First Display:**
- **Z-Test:** Shows `Input: Data` and `Stats`.
- **ω (Population mean):** 742
- **σ (Standard deviation):** 68.1
- **x̄ (Sample mean):** 763
- **n (Sample size):** 65
- Test type: Two-tailed (μ ≠ ω)

**Second Display:**
- **ω (Population mean):** 742
- **z (Z-score):** 2.486158777
- **p (P-value):** 0.0064565285
- **x̄ (Sample mean):** 763
- **n (Sample size):** 65

---

#### Finding Critical Values and Rejection Regions

For Exercises 19-24, determine the critical values and rejection regions for z-tests at various levels of significance (α). A graph should accompany your answer.

19. **Left-tailed test, α = 0.03**

20. **Left-tailed test, α = 0.09**

21. **Right-tailed test, α = 0.05**

22. **Right-tailed test, α = 0.08**

23. **Two-tailed test, α = 0.02**

24. **Two-tailed test, α = 0.12**

---

#### Graphical Analysis

For Exercises 25 and 26, determine if the standardized test statistic $ z $ allows rejection of the null hypothesis. Provide reasoning for your decision.

**Exercise 25:**
- (a) $ z = -1.301 $
- (b) $ z = 1.203 $
- (c) $ z = 1.280 $
- (d) $ z = 1.286 $

**Exercise 26:**
- (a) $ z = 1.98 $
- (b) $ z = -1.89 $
- (c) $ z = 1.65 $
- (d) $ z = -1.99 $

**Graph Explanation:**
Two bell curve graphs are displayed:
- **Graph for Exercise 25:** A standard normal distribution curve

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