Feel free to pick one of those questions-but it would be better for you to formulate a question of your own. For this assignment, you need a question related to a singleproportion(since our sample data is drawn from a single population) and one that will require the use of a confidence interval and hypothesis test to answer.
NOTE: There is a sample StatCrunch Assignment 3 designed to give you an idea of how to do this assignment. It uses a question related to the proportions of female and male students at StatCrunch U. You cannot use that question on this assignment.
- Is the proportion of female students at StatCrunch U different from the nationwide proportion of female students as reported by USA today?
- Is the proportion of seniors less than 25% of the student body?
- Is the proportion of students who work different from the nationwide proportion of students who work reported as 71% by a 2013 U.S. Census report?
- Is the proportion of students with student loans greater than the proportion of students without student loans? (This can be treated as a single proportion problem from the point of view that all students either do or do not have a student loan.
Answer each of the following questions. Point values are indicated with each question.
1. State your question. Remember that your question should be related to the population proportion or proportions and should be one that will require the use of a confidence interval and hypothesis test to answer. Assume that your sample is representative of the population.
2. Explain the methodology you will use to answer the question you posed. Your explanation should include answers to the following questions. Do not include your analysis or answers to your question here-only describe how you will do the analysis.
- What is the variable of interest?
- What confidence interval will you use?
- What are your null and alternate hypotheses?
- Is it a one-sample or two-sample test?
- Is it an upper (right)-, lower (left)-, or two-tail test?
- What level of significance will you use and why?
- Are the conditions necessary for a confidence interval and hypothesis test for the population proportion satisfied? Explain.
3. Carry out the methodology described in 2 above. Use StatCrunch and paste copies of the StatCrunch output in the space below. (NOTE: For the purposes of this assignment, go ahead and complete the confidence interval and hypothesis test even if there are not at least 10 successes and 10 failures.) Your explanation should include answers to the following questions:
- What are the upper and lower bounds of the confidence interval?
- What is the error term in the confidence interval?
- What does the confidence interval mean in terms of the question you posed?
- What is the p-value in your hypothesis test and what does it mean in terms of the question you posed?
- Did you reject or not reject the null hypothesis and why?
- What is the conclusion of your hypothesis test in terms of the question you posed?
- Do the results of the confidence interval and hypothesis test agree? Explain.
4. Based on the results of 2 and 3 above, answer your question. Include an explanation of how you used the StatCrunch output to formulate your answer.