### Statistical Hypothesis Testing#### Problem Statement**6. Suppose you are testing:**\[ H_0: p = 0.8 \quad \text{versus} \quad H_1: p < 0.8, \]where \( n = 25 \). From your data, you calculate your test statistic value as \( +1.2 \).**Tasks:**(a) Should you use \( z \) or \( t \) when finding a p-value for this scenario?(b) Calculate the p-value for this scenario.(c) Using a significance level of 0.062, what decision should you make (Reject \( H_0 \) or Do Not Reject \( H_0 \))?---#### Detailed Explanation- **Test Statistic**: We have a test statistic value of \( +1.2 \).- **Sample Size \( n \)**: 25. - **Null Hypothesis \( H_0 \)**: Population proportion \( p = 0.8 \).- **Alternative Hypothesis \( H_1 \)**: Population proportion \( p < 0.8 \).- **Significance Level**: 0.062.---#### Solution Approach1. **Choosing Between \( z \) and \( t \):** - Since we are dealing with proportions and assuming a normal approximation is valid due to reasonable sample size, use the \( z \)-test.2. **P-value Calculation:** - Use the standard normal distribution to find the p-value corresponding to a test statistic of \( +1.2 \). Since this is a one-tailed test (because \( H_1: p < 0.8 \)), the p-value is the probability that \( Z > 1.2 \).3. **Decision Making:** - Compare the p-value with the significance level (0.062). - If the p-value is less than the significance level, reject \( H_0 \). - Otherwise, do not reject \( H_0 \).Use statistical calculators or tables to determine exact values as needed.

Answered: 6. Suppose you are testing Ho: p= 0.8…

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

You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly less than 0.15. You use a significance level of a =0.02. Ho:p= 0.15 H1:p < 0.15 You obtain a sample of sizen= 504 in which there are 60 successes. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is. O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that.. O There is sufficient evidence to warrant rejection of the claim that the proportion of men oven 50 who regularly have their prostate examined is less than 0.15. There is not sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is…
You wish to test the following claim (Ha) at a significance level of a = 0.002. = Ho: P₁ Ha: P1 P2 P2 You obtain a sample from the first population with 594 successes and 78 failures. You obtain a sample from the second population with 558 successes and 44 failures. The test statistic is... O in the critical region not in the critical region critical value = test statistic = This test statistic leads to a decision to... reject the null hypothesis fail to reject the null hypothesis [three decimal accuracy] [three decimal accuracy] As such, the final conclusion is that... O There is sufficient evidence to support that the first population proportion is less than the second population proportion. There is not sufficient evidence to support that the first population proportion is less than the second population proportion.
You wish to test the following claim (HaHa) at a significance level of α=0.005. Ho:p=0.35 Ha:p≠0.35You obtain a sample of size n=650 in which there are 209 successful observations.Determine the test statistic formula for this test.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.35. There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.35. The sample data support the claim that the population proportion is not equal to 0.35. There is not…
You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly smaller than 68% at a significance level of αα = 0.05. According to your sample, 52 out of 82 potential voters prefer Candidate A. The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.)
Give one method to increase statistical power and Which test statistic should you use if you are comparing two variances?
You wish to test the following daim (Ha) at a significance level of a = 0.10. H,:P1 P2 You obtain 615 successes in a sample of size n1 = 704 from the first population. You obtain 490 successes in a sample of size n2 = 581 from the second population. critical value = [three decimal accuracy] test statistic = [three decimal accuracy] The test statistic is... O in the critical region O not in the critical region This test statistic leads to a decision to... O reject the null accept the null fail to reject the null As such, the final condusion is that... O There is sufficient evidence to support that the first population proportion is greater than the second population proportion. O There is not sufficient evidence to support that the first population proportion is greater than the second population proportion.
You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly more than 0.15. You use a significance level of a = 0.01. Но:р — 0.15 H1:p > 0.15 You obtain a sample of size n 137 in which there are 28 successes. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is.. less than (or equal to) a greater than a This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that. O There is sufficient evidence to warrant rejection of the claim that the proportion of women over 40 who regularly have mammograms is more than 0.15. O There is not sufficient evidence to warrant rejection of the claim that the proportion of women over 40 who regularly have mammograms is more than 0.15. The sample data support…
In a 2005 study 2205 adolescents aged 12 - 19 years old were give a treadmill test to check their cardiovascular health. 750 of the subjects were determined to have poor cardiovascular fitness. The researchers want to claim that more than 30% of adolescents have poor cardiovascular health (with a 5% level of significance). The research hypothesis is Ha:p>0.30. Find the test statistic, p-value, and state your conclusion.
You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly less than 0.52. You use a significance level of a = 0.01. Ho:p = 0.52 H1:p < 0.52 You obtain a sample of size n = 414 in which there are 208 successes. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) a greater than a This p-value leads to a decision to... reject the null accept the null O fail to reject the null
You are conducting a hypothesis test where alternative (research) hypothesis is that mu is greater than 850. You are testing at the 0.01 significance level. You take a sample of size 64 and calculate your test statistic to be -1.50. What would your test statistic be if you were testing, instead, at the 0.10 significance level?
You wish to test the following claim (H) at a significance level of a = 0.001. Ho: P₁ ≤ P2 Ha: P₁ P2 You obtain 194 successes in a sample of size n₁ in a sample of size n₂ = 365 from the second population. - test statistic = p-value = 240 from the first population. You obtain 273 successes [three decimal accuracy] [three decimal accuracy]
You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.16. You use a significance level of a = 0.01. Но:р — 0.16 H1:p > 0.16 You obtain a sample of size n = 621 in which there are 104 successes. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a greater than a This test statistic leads to a decision to... O reject the null O accept the null Ofail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the proportion of voters who prefer Candidate A is more than 0.16. O There is not sufficient evidence to warrant rejection of the claim that the proportion of voters who prefer Candidate A is more than 0.16. O The sample data support the claim that the…

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