StatCrunch Assignment 1 - Part B (1B) This page explains the assignment. The questions you need to answer are on the next page. A key part of research involves formulating interesting questions and then developing a methodology and collecting appropriate data to answer those questions. In this assignment, assume that you are the researcher who developed the survey you saw Part A of this assignment. Normally, you would have your research questions in mind prior to developing a survey. We will \"pretend\" that was the case, but in reality, the first thing you need to do to complete this assignment is to formulate questions that can be answered based on sample data you collected in Part A. For convenience, the survey items are shown below. Here are some questions (from the StatCrunch website) that could be answered using survey data: StatCrunch_Assignment_1B-RevTwo8-25 The items below ask you to formulate a question, describe your methodology for answering the question, carry out the methodology you described, then answer your question. Although not as detailed, this mirrors the format used in many research reports. Respond to the following items. 1. In Part A of this assignment, you selected a random sample of 30 StatCrunch U students and created a StatCrunch file containing data from the above survey for those students. You will use the StatCrunch data file you created in Part A to complete this assignment. Following the instructions at the end of Part A, paste your StatCrunch data file in the space below. This will allow your instructor to see your data. PASTE YOUR SAMPLE DATA HERE: ID Gender Class Hours Work Loans CC Debt 248 Female 4 15 0 0 4528 836 Female 3 14 0 0 4168 1072 Female 4 12 15 16357 5854 5518 Female 3 6 34.5 0 3932 5628 Female 2 15 0 9813 2414 7634 Male 2 14 0 0 3077 7683 Female 1 15 0 0 1122 7777 Female 1 9 24.5 0 0 12592 Male 1 17 0 4851 1313 12996 Female 4 15 0 0 3863 14115 Male 2 18 0 0 4769 16963 Male 1 15 0 3642 1385 17180 Male 3 13 0 0 4958 17552 Female 1 9 24.5 4309 1058 17672 Female 1 11 15.5 4351 1052 19090 Male 1 16 7 0 1759 22985 Male 1 16 0 0 0 26582 Female 3 18 6.5 0 3666 29813 Male 4 4 38 15233 4573 30282 Female 1 17 9.5 4326 1290 31215 Male 1 15 0 5827 1720 32127 Female 2 21 0 0 2444 32309 Female 2 17 19 8703 3098 38503 Male 1 15 0 0 1550 39052 Female 2 14 0 0 3024 40083 Female 3 13 0 0 2625 42569 Female 1 15 0 0 0 43604 Male 4 9 31.5 15989 7947 45125 Male 4 15 0 0 2780 45330 Female 3 15 0 0 2256 "" "" "" "" "" "" "" 2a. State a question related to a categorical variable that can be answered using your survey data and the techniques you have studied thus far in this course. You are encouraged to develop your own question, but you may use an appropriate question from the StatCrunch StatCrunch_Assignment_1B-RevTwo8-25 website. The question you use should be about the entire population of StatCrunchu students not just about those in the sample. Assume that your sample is representative of the population. How are the students distributed across the classes of Freshmen (1), Sophomore (2), Junior (3) and Senior (4)? Does the proportion of females change across the classes? b. 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 hereonly describe how you will do the analysis. What is the variable of interest? The proportion of female's students in all the classes What graphical techniques will you use to describe your data? I will use a histogram to describe my data Why are those techniques appropriate? Why did you choose them? A histogram will show the data in a clear way and I would also use a percentage instead of whole numbers due to the large amount. c. Carry out the methodology described in b above. Use StatCrunch and paste copies of the graphs/charts from StatCrunch in the space below. d. Based on the results of b and c above, answer your question. Include an explanation of how you used the graphs and charts to formulate your answer. 3a. State a question related to a numerical variable that can be answered using your survey data and the techniques you have studied thus far in this course. You are encouraged to develop your own question, but you may use an appropriate question from the StatCrunch website. The question you use should be about the entire population of StatCrunch U students not just about those in the sample. Assume that your sample is representative of the population. b. 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 hereonly describe how you will do the analysis. What is the variable of interest? What graphical techniques will you use to describe your data? Why are those techniques appropriate? Why did you choose them? What numerical measures will you use to describe your data? Why are those measures appropriate? Why did you choose them? StatCrunch_Assignment_1B-RevTwo8-25 c. Carry out the methodology described in b above. Use StatCrunch and paste copies of the graphs/charts and numerical summaries from StatCrunch in the space below. d. Based on the results of b and c above, answer your question. Include an explanation of how you used the graphs, charts, and numerical summaries to formulate your answer. StatCrunch_Assignment_1B-RevTwo8-25 StatCrunch Assignment 1 - Part B (1B) This page explains the assignment. The questions you need to answer are on the next page. A key part of research involves formulating interesting questions and then developing a methodology and collecting appropriate data to answer those questions. In this assignment, assume that you are the researcher who developed the survey you saw Part A of this assignment. Normally, you would have your research questions in mind prior to developing a survey. We will \"pretend\" that was the case, but in reality, the first thing you need to do to complete this assignment is to formulate questions that can be answered based on sample data you collected in Part A. For convenience, the survey items are shown below. Here are some questions (from the StatCrunch website) that could be answered using survey data: StatCrunch_Assignment_1B-RevTwo8-25 The items below ask you to formulate a question, describe your methodology for answering the question, carry out the methodology you described, then answer your question. Although not as detailed, this mirrors the format used in many research reports. Respond to the following items. 1. In Part A of this assignment, you selected a random sample of 30 StatCrunch U students and created a StatCrunch file containing data from the above survey for those students. You will use the StatCrunch data file you created in Part A to complete this assignment. Following the instructions at the end of Part A, paste your StatCrunch data file in the space below. This will allow your instructor to see your data. PASTE YOUR SAMPLE DATA HERE: Need the data 2a. State a question related to a categorical variable that can be answered using your survey data and the techniques you have studied thus far in this course. You are encouraged to develop your own question, but you may use an appropriate question from the StatCrunch website. The question you use should be about the entire population of StatCrunchu students not just about those in the sample. Assume that your sample is representative of the population. How are the students distributed across the classes of Freshmen (1), Sophomore (2), Junior (3) and Senior (4)? Does the proportion of females change across the classes? One example of such categorical analysis would be, does the proportion of males and females are same in Senior group. b. 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 hereonly describe how you will do the analysis. What is the variable of interest? The proportion of female's students in Senior group. What graphical techniques will you use to describe your data? I will use a pie chart to describe my data Why are those techniques appropriate? Why did you choose them? A pie chart will show the data in a clear way and I would also use a percentage instead of whole numbers due to the large amount. c. Carry out the methodology described in b above. Use StatCrunch and paste copies of the graphs/charts from StatCrunch in the space below. Need data d. Based on the results of b and c above, answer your question. Include an explanation of how you used the graphs and charts to formulate your answer. Need data StatCrunch_Assignment_1B-RevTwo8-25 3a. State a question related to a numerical variable that can be answered using your survey data and the techniques you have studied thus far in this course. You are encouraged to develop your own question, but you may use an appropriate question from the StatCrunch website. The question you use should be about the entire population of StatCrunch U students not just about those in the sample. Assume that your sample is representative of the population. Does the mean CC Debt equal in genders? b. 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 hereonly describe how you will do the analysis. What is the variable of interest? CC Debt in genders What graphical techniques will you use to describe your data? I will use a side-by-side box plot to describe my data Why are those techniques appropriate? A side-by-side box plot will show the data in a clear way and would indicate where it is significantly different or not. We can also check the skewness and normality from it. Why did you choose them? A box plot is a good representation of the quantitative data. And also is very easy to understand. What numerical measures will you use to describe your data? Based on the histogram we have to decide it. If histogram shows symmetric distribution without outliers mean and standard deviation should be used but if it shows skewed distribution median and range/IQR should be used. Why are those measures appropriate? Why did you choose them? In presence of outliers or skewed distribution mean and standard deviation gets influenced so is not a good measure. c. Carry out the methodology described in b above. Use StatCrunch and paste copies of the graphs/charts and numerical summaries from StatCrunch in the space below. Need data d. Based on the results of b and c above, answer your question. Include an explanation of how you used the graphs, charts, and numerical summaries to formulate your answer. Need data StatCrunch_Assignment_1B-RevTwo8-25 var0 ID Gender 248 Female 836 Female 1072 Female 5518 Female 5628 Female 7634 Male 7683 Female 7777 Female 12592 Male 12996 Female 14115 Male 16963 Male 17180 Male 17552 Female 17672 Female 19090 Male 22985 Male 26582 Female 29813 Male 30282 Female 31215 Male 32127 Female 32309 Female 38503 Male 39052 Female 40083 Female 42569 Female 43604 Male 45125 Male 45330 Female Class Hours 4 3 4 3 2 2 1 1 1 4 2 1 3 1 1 1 1 3 4 1 1 2 2 1 2 3 1 4 4 3 Work 15 14 12 6 15 14 15 9 17 15 18 15 13 9 11 16 16 18 4 17 15 21 17 15 14 13 15 9 15 15 Loans 0 0 15 34.5 0 0 0 24.5 0 0 0 0 0 24.5 15.5 7 0 6.5 38 9.5 0 0 19 0 0 0 0 31.5 0 0 CC Debt var8 0 4528 0 4168 16357 5854 0 3932 9813 2414 0 3077 0 1122 0 0 4851 1313 0 3863 0 4769 3642 1385 0 4958 4309 1058 4351 1052 0 1759 0 0 0 3666 15233 4573 4326 1290 5827 1720 0 2444 8703 3098 0 1550 0 3024 0 2625 0 0 15989 7947 0 2780 0 2256 StatCrunch StatCrunch Assignment 3 In this assignment, you will use the StatCrunch U data set that you developed in Module 2 as part of the first StatCrunch assignment. As you did in StatCrunch Assignment 1B, look at the items in the StatCrunch U survey and develop a question regarding population proportions that can be answered using the survey data you collected. As a reminder, here are the items on the survey: Here are some possible questions. Feel free to pick one of those questionsbut it would be better for you to formulate a question of your own. For this assignment, you need a question related to a single proportion (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. (20 pts.) 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. (30 pts.) 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 hereonly 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. (30 pts.) 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. 4. (20 pts.) 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. StatCrunch Assignment 3 Example In this assignment, you will use the StatCrunch U data set that you developed in Module 2 as part of the first StatCrunch assignment. As you did in StatCrunch Assignment 1B, look at the items in the StatCrunch U survey and develop a question regarding population proportions that can be answered using the survey data you collected. As a reminder, here are the items on the survey: Here are some possible questions. Feel free to pick one of those questionsbut it would be better for you to formulate a question of your own. For this assignment, you need a question related to a single proportion (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. Example answers follow the questions. Point values are indicated with each question. 1. (20 pts.) 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. According to a USA Today article in 2010, 57 percent of U.S. college students are female (http://www.usatoday.com/news/education/2010-01-26-genderequity26_ST_N.htm). Is the proportion of female students at StatCrunch U greater than the nationwide proportion as reported by USA Today? 2. (30 pts.) 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 hereonly describe how you will do the analysis. What is the variable of interest? The proportion of female students at StatCrunch U. What confidence interval will you use? I will use a 95% confidence interval for the population proportion. What are your null and alternate hypotheses? H0: p = .57 HA: p > .57 Is it a one-sample or two-sample test? This is a one-sample test for the population proportion. Is it an upper (right)-, lower (left)-, or two-tail test? Because the sign of the inequality in the alternate hypothesis is >, this will be a right or upper-tail test. What level of significance will you use and why? A .05 level of significance will be used. This is coincides with a 95% confidence interval and is appropriate based on the consequences of a Type I error. Are the conditions necessary for a confidence interval and hypothesis test for the population proportion satisfied? Explain. In my sample of size 30, there are 14 females and 16 males. The proportion of females in the sample is 14/30 = .467. The conditions are shown on pages 312 and 348. They are satisfied because: 1. Random Sample: The sample was randomly selected from the population of StatCrunch U students. 2. For the confidence interval, there should be at least 10 successes and 10 failures in the sample. In this case there are 14 females (success) and 16 males (failure) in the sample. For the hypothesis test there must be at least 10 expected successes and 10 expected failures in the sample if the null hypothesis is true. In this case n*p0 = 30*0.57 = 17.1 and n*(1 - p0) = 30*0.43 = 12.9, so the condition is satisfied. 3. Because sampling was done without replacement, the population must be at least 10 times larger than the sample. This is satisfied because the sample size is approximately 46,000 and the sample size is 30. 4. Items in the sample were independently selected. 5. I am assuming that the null hypothesis is true. 3. (30 pts.) 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? StatCrunch output for the confidence interval is shown below. The lower and upper bounds of the confidence interval are 0.228 and 0.645. What is the error term in the confidence interval? The error term in the confidence interval is (.6452 - .2881)/2 = .1785. What does the confidence interval mean in terms of the question you posed? I am 95% confident that the population proportion of female students at StatCrunch U is between .2881 and .6452. What is the p-value in your hypothesis test and what does it mean in terms of the question you posed? The StatCrunch output for the hypothesis test is shown below. The p-value is .8735. That means if the null hypothesis that the proportion of females in the population is .50 is true, then the probability of getting a sample proportion of females of .467 or more in a sample of size 30 is .8735. Did you reject or not reject the null hypothesis and why? The null hypothesis would not be rejected because the p-value of .8735 is greater than the level of significance of .05. What is the conclusion of your hypothesis test in terms of the question you posed? There is no evidence that the proportion of females at StatCrunch U is greater than 0.57. Do the results of the confidence interval and hypothesis test agree? Explain. The 95% confidence interval is .2881 to .6452 and we did not reject the null hypothesis that the proportion of females equals .57 at the .05 level of significance. The two agree because .57 is in the 95% confidence interval. Page 3 of 4 4. 4. (20 pts.) 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. The question asked if the proportion of female students at StatCrunch U is greater than the nationwide proportion of .57 as reported by USA Today? The 95% confidence interval contains .57 and the null hypothesis that the proportion of female students at StatCrunch U equals .57 was not rejected. Therefore there is no evidence that the proportion of female students at StatCrunch U is greater than .57. \fvar0 ID Gender 248 Female 836 Female 1072 Female 5518 Female 5628 Female 7634 Male 7683 Female 7777 Female 12592 Male 12996 Female 14115 Male 16963 Male 17180 Male 17552 Female 17672 Female 19090 Male 22985 Male 26582 Female 29813 Male 30282 Female 31215 Male 32127 Female 32309 Female 38503 Male 39052 Female 40083 Female 42569 Female 43604 Male 45125 Male 45330 Female Class Hours 4 3 4 3 2 2 1 1 1 4 2 1 3 1 1 1 1 3 4 1 1 2 2 1 2 3 1 4 4 3 Work 15 14 12 6 15 14 15 9 17 15 18 15 13 9 11 16 16 18 4 17 15 21 17 15 14 13 15 9 15 15 Loans 0 0 15 34.5 0 0 0 24.5 0 0 0 0 0 24.5 15.5 7 0 6.5 38 9.5 0 0 19 0 0 0 0 31.5 0 0 CC Debt var8 0 4528 0 4168 16357 5854 0 3932 9813 2414 0 3077 0 1122 0 0 4851 1313 0 3863 0 4769 3642 1385 0 4958 4309 1058 4351 1052 0 1759 0 0 0 3666 15233 4573 4326 1290 5827 1720 0 2444 8703 3098 0 1550 0 3024 0 2625 0 0 15989 7947 0 2780 0 2256 var0 ID Gender 248 Female 836 Female 1072 Female 5518 Female 5628 Female 7634 Male 7683 Female 7777 Female 12592 Male 12996 Female 14115 Male 16963 Male 17180 Male 17552 Female 17672 Female 19090 Male 22985 Male 26582 Female 29813 Male 30282 Female 31215 Male 32127 Female 32309 Female 38503 Male 39052 Female 40083 Female 42569 Female 43604 Male 45125 Male 45330 Female Class Hours 4 3 4 3 2 2 1 1 1 4 2 1 3 1 1 1 1 3 4 1 1 2 2 1 2 3 1 4 4 3 Work 15 14 12 6 15 14 15 9 17 15 18 15 13 9 11 16 16 18 4 17 15 21 17 15 14 13 15 9 15 15 Loans 0 0 15 34.5 0 0 0 24.5 0 0 0 0 0 24.5 15.5 7 0 6.5 38 9.5 0 0 19 0 0 0 0 31.5 0 0 CC Debt var8 0 4528 0 4168 16357 5854 0 3932 9813 2414 0 3077 0 1122 0 0 4851 1313 0 3863 0 4769 3642 1385 0 4958 4309 1058 4351 1052 0 1759 0 0 0 3666 15233 4573 4326 1290 5827 1720 0 2444 8703 3098 0 1550 0 3024 0 2625 0 0 15989 7947 0 2780 0 2256 StatCrunch StatCrunch Assignment 3 In this assignment, you will use the StatCrunch U data set that you developed in Module 2 as part of the first StatCrunch assignment. As you did in StatCrunch Assignment 1B, look at the items in the StatCrunch U survey and develop a question regarding population proportions that can be answered using the survey data you collected. As a reminder, here are the items on the survey: Here are some possible questions. Feel free to pick one of those questionsbut it would be better for you to formulate a question of your own. For this assignment, you need a question related to a single proportion (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. (20 pts.) 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. (30 pts.) 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 hereonly 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. (30 pts.) 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. 4. (20 pts.) 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. StatCrunch Assignment 3 Example In this assignment, you will use the StatCrunch U data set that you developed in Module 2 as part of the first StatCrunch assignment. As you did in StatCrunch Assignment 1B, look at the items in the StatCrunch U survey and develop a question regarding population proportions that can be answered using the survey data you collected. As a reminder, here are the items on the survey: Here are some possible questions. Feel free to pick one of those questionsbut it would be better for you to formulate a question of your own. For this assignment, you need a question related to a single proportion (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. Example answers follow the questions. Point values are indicated with each question. 1. (20 pts.) 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. According to a USA Today article in 2010, 57 percent of U.S. college students are female (http://www.usatoday.com/news/education/2010-01-26-genderequity26_ST_N.htm). Is the proportion of female students at StatCrunch U greater than the nationwide proportion as reported by USA Today? 2. (30 pts.) 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 hereonly describe how you will do the analysis. What is the variable of interest? The proportion of female students at StatCrunch U. What confidence interval will you use? I will use a 95% confidence interval for the population proportion. What are your null and alternate hypotheses? H0: p = .57 HA: p > .57 Is it a one-sample or two-sample test? This is a one-sample test for the population proportion. Is it an upper (right)-, lower (left)-, or two-tail test? Because the sign of the inequality in the alternate hypothesis is >, this will be a right or upper-tail test. What level of significance will you use and why? A .05 level of significance will be used. This is coincides with a 95% confidence interval and is appropriate based on the consequences of a Type I error. Are the conditions necessary for a confidence interval and hypothesis test for the population proportion satisfied? Explain. In my sample of size 30, there are 14 females and 16 males. The proportion of females in the sample is 14/30 = .467. The conditions are shown on pages 312 and 348. They are satisfied because: 1. Random Sample: The sample was randomly selected from the population of StatCrunch U students. 2. For the confidence interval, there should be at least 10 successes and 10 failures in the sample. In this case there are 14 females (success) and 16 males (failure) in the sample. For the hypothesis test there must be at least 10 expected successes and 10 expected failures in the sample if the null hypothesis is true. In this case n*p0 = 30*0.57 = 17.1 and n*(1 - p0) = 30*0.43 = 12.9, so the condition is satisfied. 3. Because sampling was done without replacement, the population must be at least 10 times larger than the sample. This is satisfied because the sample size is approximately 46,000 and the sample size is 30. 4. Items in the sample were independently selected. 5. I am assuming that the null hypothesis is true. 3. (30 pts.) 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? StatCrunch output for the confidence interval is shown below. The lower and upper bounds of the confidence interval are 0.228 and 0.645. What is the error term in the confidence interval? The error term in the confidence interval is (.6452 - .2881)/2 = .1785. What does the confidence interval mean in terms of the question you posed? I am 95% confident that the population proportion of female students at StatCrunch U is between .2881 and .6452. What is the p-value in your hypothesis test and what does it mean in terms of the question you posed? The StatCrunch output for the hypothesis test is shown below. The p-value is .8735. That means if the null hypothesis that the proportion of females in the population is .50 is true, then the probability of getting a sample proportion of females of .467 or more in a sample of size 30 is .8735. Did you reject or not reject the null hypothesis and why? The null hypothesis would not be rejected because the p-value of .8735 is greater than the level of significance of .05. What is the conclusion of your hypothesis test in terms of the question you posed? There is no evidence that the proportion of females at StatCrunch U is greater than 0.57. Do the results of the confidence interval and hypothesis test agree? Explain. The 95% confidence interval is .2881 to .6452 and we did not reject the null hypothesis that the proportion of females equals .57 at the .05 level of significance. The two agree because .57 is in the 95% confidence interval. Page 3 of 4 4. 4. (20 pts.) 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. The question asked if the proportion of female students at StatCrunch U is greater than the nationwide proportion of .57 as reported by USA Today? The 95% confidence interval contains .57 and the null hypothesis that the proportion of female students at StatCrunch U equals .57 was not rejected. Therefore there is no evidence that the proportion of female students at StatCrunch U is greater than .57