26. (a) z = 1.98 (b) z -1.89 (c) z 1.65 (d) z = -1.99 -3 /2 7o = 1.96 13 -1.96
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.
question 26
![**Finding Critical Values and Rejection Regions**
In Exercises 19–24, find the critical value(s) and rejection region(s) for the type of z-test with the level of significance α. Include a graph with 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**
In Exercises 25 and 26, state whether each standardized test statistic z allows you to reject the null hypothesis. Explain your reasoning.
25.
(a) z = -1.301
(b) z = 1.203
(c) z = 1.280
(d) z = 1.286
Graph Explanation (Exercise 25):
The graph shows a normal distribution curve with a shaded region in the left tail. The critical value is marked as z₀ = 1.285.
26.
(a) z = 1.98
(b) z = -1.89
(c) z = 1.65
(d) z = -1.99
Graph Explanation (Exercise 26):
The graph illustrates a normal distribution curve with shaded regions in both tails. The critical values are marked as ±z₀ = 1.96.
**Instructions for Exercises 27–30**
Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F423e8e72-9a79-41d5-aebf-65315d7e1dd6%2Ff1ea25df-a541-403c-9370-3e3f3ad809b0%2Fz0qv3q9.jpeg&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)