Consider the hypotheses below.  H0 u = 50. H0 u≠ 50  Given that x= 53, s= 20, n= 25, and a= 0.05, answer the questions below.  a) what conclusions should be drawn  b) use technology to determine the p value for this test   Please help i am having trouble and keep getting it wrong

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

Consider the hypotheses below. 

H0 u = 50. H0 u≠ 50 

Given that x= 53, s= 20, n= 25, and a= 0.05, answer the questions below. 

a) what conclusions should be drawn 

b) use technology to determine the p value for this test

 

Please help i am having trouble and keep getting it wrong ! 

**Statistical Hypothesis Testing: Problem Setup**

Consider the hypotheses below:

- Null Hypothesis (\( H_0 \)): \( \mu = 50 \)
- Alternative Hypothesis (\( H_1 \)): \( \mu \neq 50 \)

Given:
- Sample mean (\( \bar{x} \)) = 53
- Standard deviation (\( s \)) = 20
- Sample size (\( n \)) = 25
- Significance level (\( \alpha \)) = 0.05

### Questions to Answer:

**a.** What conclusion should be drawn?

**b.** Use technology to determine the p-value for this test.

---

**Answer Part a: Determine the Critical Value(s)**

- **Critical value(s):**  
  (Round to three decimal places as needed. Use a comma to separate answers as needed.)

- **Determine the Test Statistic, \( t_x \):**  
  \( t_x \) =  
  (Round to two decimal places as needed.)

### Conclusion:

Choose the correct answer:

- **A.** Do not reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
- **B.** Reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
- **C.** Do not reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \).
- **D.** Reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \). 

**Note:** Use statistical software or tables to find the exact critical values, test statistic, and p-value to reach a conclusion.
Transcribed Image Text:**Statistical Hypothesis Testing: Problem Setup** Consider the hypotheses below: - Null Hypothesis (\( H_0 \)): \( \mu = 50 \) - Alternative Hypothesis (\( H_1 \)): \( \mu \neq 50 \) Given: - Sample mean (\( \bar{x} \)) = 53 - Standard deviation (\( s \)) = 20 - Sample size (\( n \)) = 25 - Significance level (\( \alpha \)) = 0.05 ### Questions to Answer: **a.** What conclusion should be drawn? **b.** Use technology to determine the p-value for this test. --- **Answer Part a: Determine the Critical Value(s)** - **Critical value(s):** (Round to three decimal places as needed. Use a comma to separate answers as needed.) - **Determine the Test Statistic, \( t_x \):** \( t_x \) = (Round to two decimal places as needed.) ### Conclusion: Choose the correct answer: - **A.** Do not reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \). - **B.** Reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \). - **C.** Do not reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \). - **D.** Reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean differs from \( \mu = 50 \). **Note:** Use statistical software or tables to find the exact critical values, test statistic, and p-value to reach a conclusion.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Proportions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman