Homework Help is Here – Start Your Trial Now!
Math
Statistics
The proportion p of residents in a community who recycle has traditionally been 60%. A policy maker claims that the proportion is less than 60% now that one of the recycling centers has been relocated. If 116 out of a random sample of 225 residents in the community said they recycle, is there enough evidence to support the policy maker's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. HO H:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Is there enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 60%? OYes O No μ X 0 0=0 X O 00 OSO 0<0 Р 3 59 020 >O

The proportion p of residents in a community who recycle has traditionally been 60%. A policy maker claims that the proportion is less than 60% now that one of the recycling centers has been relocated. If 116 out of a random sample of 225 residents in the community said they recycle, is there enough evidence to support the policy maker's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. HO H:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Is there enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 60%? OYes O No μ X 0 0=0 X O 00 OSO 0<0 Р 3 59 020 >O

MATLAB: An Introduction with Applications
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
icon
Related questions
Question
The task is to determine whether there is enough evidence to support a policy maker's claim regarding the proportion of residents in a community who recycle. The claim is that the proportion is now less than 60% after the relocation of recycling centers. The relevant data shows that 116 out of a random sample of 225 residents said they recycle. This requires performing a one-tailed test at the 0.01 level of significance. ### Step-by-Step Analysis: **(a) Hypotheses:** - Null Hypothesis (\(H_0\)): \(p \geq 0.60\) - Alternative Hypothesis (\(H_1\)): \(p < 0.60\) **(b) Type of Test Statistic:** - Choose the appropriate test statistic, typically a z-test for proportions. **(c) Calculate Test Statistic:** - Input the formula and calculate the z-value. - Round off your answer to three or more decimal places. **(d) Calculate p-value:** - Determine the probability associated with the test statistic. - Round your answer to at least three decimal places. **(e) Decision:** - Based on the p-value and the significance level (\(\alpha = 0.01\)), decide if there is sufficient evidence to support the policy maker's claim. - Select either Yes or No. **Additional Visuals:** A visual tool with various symbols (µ, \(\hat{p}\), \( \bar{x} \), \(\sigma\), etc.) is provided for hypothesis expressions and calculations. **Conclusion:** Answer the question: "Is there enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 60%?" and select Yes or No. Finally, options are available for saving the work or submitting the assignment.
Transcribed Image Text:The task is to determine whether there is enough evidence to support a policy maker's claim regarding the proportion of residents in a community who recycle. The claim is that the proportion is now less than 60% after the relocation of recycling centers. The relevant data shows that 116 out of a random sample of 225 residents said they recycle. This requires performing a one-tailed test at the 0.01 level of significance. ### Step-by-Step Analysis: **(a) Hypotheses:** - Null Hypothesis (\(H_0\)): \(p \geq 0.60\) - Alternative Hypothesis (\(H_1\)): \(p < 0.60\) **(b) Type of Test Statistic:** - Choose the appropriate test statistic, typically a z-test for proportions. **(c) Calculate Test Statistic:** - Input the formula and calculate the z-value. - Round off your answer to three or more decimal places. **(d) Calculate p-value:** - Determine the probability associated with the test statistic. - Round your answer to at least three decimal places. **(e) Decision:** - Based on the p-value and the significance level (\(\alpha = 0.01\)), decide if there is sufficient evidence to support the policy maker's claim. - Select either Yes or No. **Additional Visuals:** A visual tool with various symbols (µ, \(\hat{p}\), \( \bar{x} \), \(\sigma\), etc.) is provided for hypothesis expressions and calculations. **Conclusion:** Answer the question: "Is there enough evidence to support the policy maker's claim that the proportion of residents who recycle is less than 60%?" and select Yes or No. Finally, options are available for saving the work or submitting the assignment.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar 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
SEE MORE TEXTBOOKS