**Exercise 5: Hypothesis Testing Using T-Distribution**---**Context:**This exercise involves conducting hypothesis tests based on a random sample drawn from an approximately normal population with an unknown standard deviation. The task is to determine the p-value for each scenario described, and visually represent this by drawing a t-curve and shading the region corresponding to the p-value.**Instructions:**For each set of hypotheses, sample size, and T-statistic given below, follow these steps:1. Determine the p-value.2. Draw a t-distribution curve.3. Shade the region under the curve that corresponds to the p-value.Note: Since precise p-values cannot always be determined using t-tables, providing a range suffices.---**Scenarios:**(a) **Hypothesis:** \( H_A : \mu > 0.5 \) **Sample Size:** \( n = 26 \) **T-Statistic:** \( T = 2.6 \)(b) **Hypothesis:** \( H_A : \mu \neq 0.5 \) **Sample Size:** \( n = 26 \) **T-Statistic:** \( T = 2.6 \)(c) **Hypothesis:** \( H_A : \mu < 3 \) **Sample Size:** \( n = 18 \) **T-Statistic:** \( T = -2.2 \)(d) **Hypothesis:** \( H_A : \mu < 3 \) **Sample Size:** \( n = 18 \) **T-Statistic:** \( T = 2.2 \)---**Graphical Explanation:**For each scenario, the following should be depicted:1. **T-Curve:** - The curve is symmetrical around zero and represents the t-distribution specific to the degrees of freedom corresponding to each sample size.2. **Shaded Region:** - For a one-tailed test (as in cases (a) and (c)), shade the area in the direction of the alternative hypothesis. - For a two-tailed test (as in case (b)), shade both tails of the distribution. - The area shaded represents the probability related to the calculated T-statistic.---Using this setup, visually and analytically interpret each scenario to gain insight into the hypothesis testing framework using the t-distribution.

Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Answered: 5. Not self-graded (Revision of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

If a Type I error is made, what conclusion will be drawn regarding the mean breaking strength?
Use the 1odwing Wildlife: Coyotes A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be z = 2.05 years, with sample standard deviation 8 = 0.82 years (based on information from the book Coyotes: Biology, Behavior and Management by M. Bekoff, Academic Press). However, it is thought that the overall population mean age of coyotes is µ=1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a = 0.01. Fl in the blanks a 007 • Ho u- 175 years * H u> 176 yean QUESTION 7 What is your test statistic? (t-statistic) 2.48 QUESTION 8 What is your p-value? (Hint You will need the degrees of freedom to find the p-value.) <0.01d QUESTION 9 Do you reject the null hypothesis? O Yes No
You are part of a trivia team and have tracked your team's performance since you started playing, so you know that your scores are normally distributed with u = 88 and a = 15 Recently, a new person joined the team, and you think the scores have changed Sample data is: n = 28, sample mean = 72 Assuming a two tailed test, What is the test statistic (Z)?
The mean score on a driving exam for a group of driver’s education students is 76 points, with a standard deviation of 6 points. Apply chebychev’s theorem to the data using K=2. Interpret, At least ___% of the exam score falls between ___and ____
How do you find (b.)?
10) A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 40 mi/hr. A random sample of 15 vehicles has a mean speed of 43 mil/hr and a standard deviation of 4.4 mi/hr. Assume that speeds follow a normal distribution. What statistical test should be used to test the claim? (pick one of the options) 1. t-test 2. 2.73 3. 15 4. 10.9 5. 14 6. z-test 7. 2.52 8. 2.64 Calculate the value of standardized test statistic. (pick one of the options) 1. t-test 2. 2.73 3. 15 4. 10.9 5. 14 6. z-test 7. 2.52 8. 2.64 What is the degree of the freedom for the distribution of the test statistics. (pick one of the options) 1. t-test 2. 2.73 3. 15 4. 10.9 5. 14 6. z-test 7. 2.52 8. 2.64
Please sir or ma’am, please help me with hypothesis, critical region, and t statistic.
In a test, the average score is 100. You believe that the average score for your class is higher. You took a sample of 30 students. The average score for this group is 140 with a standard deviation of 15. Test the hypothesis that the average score is greater. Use a = The rejection region for the test statistic is... .05. less than -1.959963985 and greater than 1.959963985 less than - 2.045229642 and greater than 2.045229642 less than - 1.644853627 and greater than 1.644853627 none of the above O O O O
A random sample of n1 = 49 measurements from a population with population standard deviation ?1 = 3 had a sample mean of x1 = 10. An independent random sample of n2 = 64 measurements from a second population with population standard deviation ?2 = 4 had a sample mean of x2 = 12. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements: What distribution does the sample test statistic follow? Explain. The Student's t. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. (b) State the hypotheses. H0: ?1 = ?2;…
Determine the cri tical z-score corresponding to a = 0.2 in a left-tail test. crititical z-score = [three decimal accuracy]
17. Question content area top Part 1 Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ=52,400; α=0.10 Sample statistics: x=53,647, s=3000, n=20 LOADING... Click the icon to view the t-distribution table. Question content area bottom Part 1 What are the null and alternative hypotheses? Choose the correct answer below. A. H0: μ≠52,400 Ha: μ=52,400 B. H0: μ≥52,400 Ha: μ<52,400 C. H0: μ=52,400 Ha: μ≠52,400 D. H0: μ≤52,400 Ha: μ>52,400 Part 2 What is the value of the standardized test statistic? The standardized test statistic is enter your response here . (Round to two decimal places as needed.) Part 3 What is(are) the critical value(s)? The critical value(s) is(are) enter your response here . (Round to three decimal places as needed. Use…
I need help only with the lat part of the exercise

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS