Math 227B Project 1 Inferences on a Population Parameter In this project, you will draw inferences on a population parameter: proportion or mean. You will describe a problem including a general claim made about a population parameter, collect data, test hypothesis, and construct and interpret a confidence interval to determine whether the claim made about a population parameter can still be supported by the sample collected. You will, then, write a report on your findings including all the required components below and turn in by the stated due date according to the guidelines provided in this paper. Required components: 1. Understand the Problem a) Select a parameter of your choice: proportion or mean for which a general claim can be (or has been) made. Please try to decide on something that you are interested in knowing about. Who (what) is the population of your choice? b) Describe the problem including a general claim made about the specific population: Examples for testing a claim about the population: Proportion: Do the majority of community college students qualify for federal student loans? Mean: Has the average birth weight in a town decreased from 3,500 grams? c) Identify any relevant variable to the above problem: Are the variable categorical or numerical? d) Collect either categorical or numerical data, at least 30 data values. Discuss how your data has been collected and whether you were able to collect a random sample of data. If a random sampling was not possible, please explain why not. 2. Analyze the Data a) Discuss whether required conditions are met to test hypotheses depending on the parameter being addressed.

	Population Proportion (Section 10.2)	Population Mean (Section 10.3)
Required Conditions for hypotheses testing and construction a confidence interval	*The sample is a simple random sample. * *The sample size is no more than 5% of population size.(Independent)	*The sample size is greater than 30 or the population is normally distributed
Distributions (Test Statistic)	z-distribution	Students t-distribution

b) Test hypotheses using

• Determine the null and alternative hypotheses. Use proper symbols.
• Use technology to find the test statistics.
• Use technology to find the P-value. Provide the meaning of the P-value about your problem. Also, provide a list of steps in finding the P-value using StatCrunch.
• Make the decision on whether to reject the null hypothesis or not.

Provide a statement whether the claim made about the population parameter can still be supported by the sample collected.Do you think your conclusion was due to the sampling variability (random chance) or do you think the data from the sample is indeed significant and it suggests that the population parameter needs to be rejected? Explain according to the P-value.

• State the conclusion about the claim.

c) Construct and interpret a 95% confidence interval for the population parameter.

• Determine the point estimate of the population parameter.
• State the confidence interval. Also, provide a list of steps in constructing the confidence interval using StatCrunch.
• Interpret the confidence interval about your problem.
• Does the confidence interval support the conclusion of the hypothesis testing? Explain your answer.

3. Draw Conclusions a) What do the results you got indicate about the inference on the population parameter? Decide whether the claim made about the population parameter can still be supported by the samples collected. Explain using the results of the hypothesis testing and the confidence interval. b) If it is relevant or meaningful in context, think of a way that these results could be used in practice. 4. Summarize Write a short summary of the main findings that you discovered. Grades will be based on: 1. Explanation of your topic and appropriate responses in part 1 Understanding the problem [10 pts], 2. Relevance and completeness of the analysis of the data including appropriate responses in part 2 Analyze the paired Data [50 pts], 3. Completeness and appropriateness of drawing conclusions in part 3 Draw conclusions [20 pts], 4. Clear summary of the main findings in part 4 Summarize [10 pts], and 5. Overall quality of the report and adherence of the project guidelines [10 pts] Submission Guidelines and the due date: The report must be generated using computer and the report should contain the title, your name, date, course name and instructors name. The report should not contain any misspelled words. The project score sheet along with the title of your project and the website where you collected or found your data (page 4 of this guidelines), must be submitted to the instructor by: ______________ The project is due at the beginning of the lab on: ______________ Note: Late submission will be accepted. However, there will be 10% per day penalty from your final project grade. Math 227B Project Inferences on a Population Parameter - Score Sheet (Total 100 points) Name:________________________________________ Date:__________________________________ Title of the project: ____________________________________________________________________ Website where you found the data:_______________________________________________________ Project Grade: __________________________________

Required Tasks	Grading criteria	Comments/Scores
1. Understand the Problem a) Select a parameter of your choice: proportion or mean for which a general claim can be (or has been) made. Please try to decide on something that you are interested in knowing about. Who (what) is the population of your choice? b) Describe the problem including a general claim made about the specific population: c) Identify any relevant variable to the above problem: Are the variable categorical or numerical? d) Collect either categorical or numerical data, at least 30 data values. Discuss how your data has been collected and whether you were able to collect a random sample of data. If a random sampling was not possible, please explain why not.	1. Explanation of your topic and appropriate responses in step 1 Understanding the problem [10 pts]
2. Analyze the paired Data a) Discuss whether required conditions are met to test hypothesis depending on the parameter being addressed. b) Test hypotheses using Determine the null and alternative hypotheses. Use proper symbols. Use technology to find the test statistics. Use technology to find the P-value. Provide the meaning of the P-value about your problem. Also, provide a list of steps in finding the P-value using StatCrunch. Make the decision on whether to reject the null hypothesis or not. Provide a statement whether the claim made about the population parameter can still be supported by the sample collected.Do you think your conclusion was due to the sampling variability (random chance) or do you think the data from the sample is indeed significant and it suggests that the population parameter needs to be rejected? Explain according to the P-value. State the conclusion about the claim. c) Construct and interpret a 95% confidence interval for the population parameter. Determine the point estimate of the population parameter. State the confidence interval. Also, provide a list of steps in constructing the confidence interval using StatCrunch. Interpret the confidence interval about your problem. Does the confidence interval support the conclusion of the hypothesis testing? Explain your answer.	2. Relevance and completeness of the analysis of the data including appropriate responses in step 2 Analyze the paired Data [50 pts]
3. Draw Conclusions a) What do the results you got indicate about the inference on comparing two population parameters? Decide whether the claim made about two population parameters can still be supported by the samples collected. Explain using the results of the hypothesis testing and the confidence interval. b) If it is relevant or meaningful in context, think of a way that these results could be used in practice.	3. Completeness and appropriateness of drawing conclusions in step 3 Draw conclusions [20 pts]
4. Summarize Write a short summary of the main findings that you discovered.	4. Clear summary of the main findings in step 4 Summarize [10 pts]
5. Overall quality of the report	5. Overall quality of the report and adherence of the project guidelines [10 pts]