please answer the MATH2208 LAB 9 carefully. and find the note for the chapters 16 and 17.

Wednesday, November 11 Name: _________________________ MATH2208 Lab 9 Lab Section:___________ Please read all of these instructions before beginning your lab. This lab is due by 12 p.m. (noon) on Friday, November 13. Labs can be uploaded to Moodle, or dropped off to the lab room during regular lab times on Thursday or Friday. You cannot drop your lab off to your lab instructor’s office; it must be taken to the lab room. You may have someone drop your lab off for you, but they will be asked to initial the sign out sheet. This lab assignment is for students registered in a Wednesday lab section only. Students who take labs on other days are expected to be at their regularly scheduled lab this week. If you have questions, you may email the lab instructor ([email protected]) Labs submitted must be your own work. You are welcome to work with a small group like you would in lab, but you must write/type your own answers. Your lab section is required. If you do not know your lab section letter, the time of your lab is fine. Question 1 Many university students travel to attend school. At the first lab this term, we asked Intro stats students at MSVU if English is their first language. We randomly selected 60 of the students who took the survey this term, and found that 49 of them said that English is their first language. [Note: this is a different sample of the same students discussed in Question 3 of Lab 8] Here is the Minitab output for this data: Test and CI for One Proportion Sample X N Sample p 95% CI 1 49 60 0.816667 (0.718759, 0.914574) Using the normal approximation. a. Confirm that the assumptions are satisfied by stating the appropriate condition(s) and explaining in context. Independence Assumption: Sample Size Assumption: b. Interpret the confidence interval [hint: the interval is on the Minitab output above; you do not need to calculate it] c. What does 95 % confidence mean in the context of this question? (note: we are looking for a definition here, not an interpretation) d. What would happen to the confidence interval if the level of confidence is increased? Explain. e. What would happen to the confidence interval if the sample size decreased? Explain. f. What is the margin of error for the 95% confidence interval above? Show your work. g. How large a sample would we need to take if we wished to maintain a 95% level of confidence with a margin of error of 3%? You may use the sample above as a pilot study. Show your work, including the formula. n = _____________ h. Is the sample size in (g) bigger or smaller than the sample size used to calculate the confidence interval? BIGGER SMALLER What does this imply about the margin of error found in part (f)? Is this consistent with your answer to part (f)? Explain. Question 2 Recently, the re-appearance of several childhood illness has raised concerns about the immunization program in Nova Scotia. The Minister of Health wishes to estimate the proportion of families in Nova Scotia who do follow the recommended immunization schedule. In a random sample of 110 families from a large Family Practice (doctor’s office with more than one doctor on staff) in Nova Scotia, 104 reported that they follow the recommendation about childhood immunization. Test and CI for One Proportion Sample X N Sample p 95% CI 1 104 110 0.945455 (0.903017, 0.987892) Using the normal approximation. The five statements below are related to a 95% confidence interval for this data. Label each statement true or false. If the statement is false, explain why it is false. a. The Minister of Health is 95% certain that the proportion of the 110 families follow the recommended immunization schedule is between 0.90 and 0.99. b. The Minitab of Health is 95% certain that the proportion of the 110 families who follow the recommended immunization schedule is 0.95. c. Assuming that a normal model can be used, the Minister of Health is 95% certain that the proportion of all families in Nova Scotia who follow the recommended immunization schedule will be between 90% and 99%. d. Assume that a normal model can be used. The Minister of Health is more than 95% certain the proportion of families in Nova Scotia who follow the recommended immunization schedule will be in this range. e. Assuming that a normal model can be used, the Minister of Health is 95% certain that the proportion of all families in Canada who follow the recommended immunization schedule will be between 90% and 99%. Question 3 Each of the three situations below requires a hypothesis test about a population proportion. In each case, state the appropriate null hypothesis (Ho) and alternative hypothesis (Ha) in symbols. For part (a) only, also define the parameter (p). a. A city claims that 75% of all low income housing is 1500 sq. ft. The tenants believe the proportion of housing this size is smaller than the claim, and hire an independent firm to test an appropriate hypothesis. b. To maintain good oral health, the Canadian Dental Association recommends brushing, flossing, regular check-ups, and cleaning by a dentist. Although the cost for preventative dental care can be less than the eventual cost for the treatment of problems caused by neglect, many students simply cannot afford to go to the dentist every year. Past records from the CDA show that 55% of university students visit the dentist on a yearly basis. The Association is interested in whether this proportion has changed. c. A large software company gives job applicants a test of programming ability, and the pass rate for the test has been 80% in the past. A statistical analyst in the company conducts a study using this year’s applicant data to see if there evidence to indicate that the pass rate has increased. Wednesday, November 11 Name: _________________________ MATH2208 Lab 9 Lab Section:___________ Please read all of these instructions before beginning your lab. This lab is due by 12 p.m. (noon) on Friday, November 13. Labs can be uploaded to Moodle, or dropped off to the lab room during regular lab times on Thursday or Friday. You cannot drop your lab off to your lab instructor’s office; it must be taken to the lab room. You may have someone drop your lab off for you, but they will be asked to initial the sign out sheet. This lab assignment is for students registered in a Wednesday lab section only. Students who take labs on other days are expected to be at their regularly scheduled lab this week. If you have questions, you may email the lab instructor ([email protected]) Labs submitted must be your own work. You are welcome to work with a small group like you would in lab, but you must write/type your own answers. Your lab section is required. If you do not know your lab section letter, the time of your lab is fine. Question 1 Many university students travel to attend school. At the first lab this term, we asked Intro stats students at MSVU if English is their first language. We randomly selected 60 of the students who took the survey this term, and found that 49 of them said that English is their first language. [Note: this is a different sample of the same students discussed in Question 3 of Lab 8] Here is the Minitab output for this data: Test and CI for One Proportion Sample X N Sample p 95% CI 1 49 60 0.816667 (0.718759, 0.914574) Using the normal approximation. a. Confirm that the assumptions are satisfied by stating the appropriate condition(s) and explaining in context. Independence Assumption: Sample Size Assumption: b. Interpret the confidence interval [hint: the interval is on the Minitab output above; you do not need to calculate it] c. What does 95 % confidence mean in the context of this question? (note: we are looking for a definition here, not an interpretation) d. What would happen to the confidence interval if the level of confidence is increased? Explain. e. What would happen to the confidence interval if the sample size decreased? Explain. f. What is the margin of error for the 95% confidence interval above? Show your work. g. How large a sample would we need to take if we wished to maintain a 95% level of confidence with a margin of error of 3%? You may use the sample above as a pilot study. Show your work, including the formula. n = _____________ h. Is the sample size in (g) bigger or smaller than the sample size used to calculate the confidence interval? BIGGER SMALLER What does this imply about the margin of error found in part (f)? Is this consistent with your answer to part (f)? Explain. Question 2 Recently, the re-appearance of several childhood illness has raised concerns about the immunization program in Nova Scotia. The Minister of Health wishes to estimate the proportion of families in Nova Scotia who do follow the recommended immunization schedule. In a random sample of 110 families from a large Family Practice (doctor’s office with more than one doctor on staff) in Nova Scotia, 104 reported that they follow the recommendation about childhood immunization. Test and CI for One Proportion Sample X N Sample p 95% CI 1 104 110 0.945455 (0.903017, 0.987892) Using the normal approximation. The five statements below are related to a 95% confidence interval for this data. Label each statement true or false. If the statement is false, explain why it is false. a. The Minister of Health is 95% certain that the proportion of the 110 families follow the recommended immunization schedule is between 0.90 and 0.99. b. The Minitab of Health is 95% certain that the proportion of the 110 families who follow the recommended immunization schedule is 0.95. c. Assuming that a normal model can be used, the Minister of Health is 95% certain that the proportion of all families in Nova Scotia who follow the recommended immunization schedule will be between 90% and 99%. d. Assume that a normal model can be used. The Minister of Health is more than 95% certain the proportion of families in Nova Scotia who follow the recommended immunization schedule will be in this range. e. Assuming that a normal model can be used, the Minister of Health is 95% certain that the proportion of all families in Canada who follow the recommended immunization schedule will be between 90% and 99%. Question 3 Each of the three situations below requires a hypothesis test about a population proportion. In each case, state the appropriate null hypothesis (Ho) and alternative hypothesis (Ha) in symbols. For part (a) only, also define the parameter (p). a. A city claims that 75% of all low income housing is 1500 sq. ft. The tenants believe the proportion of housing this size is smaller than the claim, and hire an independent firm to test an appropriate hypothesis. b. To maintain good oral health, the Canadian Dental Association recommends brushing, flossing, regular check-ups, and cleaning by a dentist. Although the cost for preventative dental care can be less than the eventual cost for the treatment of problems caused by neglect, many students simply cannot afford to go to the dentist every year. Past records from the CDA show that 55% of university students visit the dentist on a yearly basis. The Association is interested in whether this proportion has changed. c. A large software company gives job applicants a test of programming ability, and the pass rate for the test has been 80% in the past. A statistical analyst in the company conducts a study using this year’s applicant data to see if there evidence to indicate that the pass rate has increased. Wednesday, November 11 Name: _________________________ MATH2208 Lab 9 Lab Section:___________ Please read all of these instructions before beginning your lab. This lab is due by 12 p.m. (noon) on Friday, November 13. Labs can be uploaded to Moodle, or dropped off to the lab room during regular lab times on Thursday or Friday. You cannot drop your lab off to your lab instructor’s office; it must be taken to the lab room. You may have someone drop your lab off for you, but they will be asked to initial the sign out sheet. This lab assignment is for students registered in a Wednesday lab section only. Students who take labs on other days are expected to be at their regularly scheduled lab this week. If you have questions, you may email the lab instructor ([email protected]) Labs submitted must be your own work. You are welcome to work with a small group like you would in lab, but you must write/type your own answers. Your lab section is required. If you do not know your lab section letter, the time of your lab is fine. Question 1 Many university students travel to attend school. At the first lab this term, we asked Intro stats students at MSVU if English is their first language. We randomly selected 60 of the students who took the survey this term, and found that 49 of them said that English is their first language. [Note: this is a different sample of the same students discussed in Question 3 of Lab 8] Here is the Minitab output for this data: Test and CI for One Proportion Sample X N Sample p 95% CI 1 49 60 0.816667 (0.718759, 0.914574) Using the normal approximation. a. Confirm that the assumptions are satisfied by stating the appropriate condition(s) and explaining in context. Independence Assumption: Sample Size Assumption: b. Interpret the confidence interval [hint: the interval is on the Minitab output above; you do not need to calculate it] c. What does 95 % confidence mean in the context of this question? (note: we are looking for a definition here, not an interpretation) d. What would happen to the confidence interval if the level of confidence is increased? Explain. e. What would happen to the confidence interval if the sample size decreased? Explain. f. What is the margin of error for the 95% confidence interval above? Show your work. g. How large a sample would we need to take if we wished to maintain a 95% level of confidence with a margin of error of 3%? You may use the sample above as a pilot study. Show your work, including the formula. n = _____________ h. Is the sample size in (g) bigger or smaller than the sample size used to calculate the confidence interval? BIGGER SMALLER What does this imply about the margin of error found in part (f)? Is this consistent with your answer to part (f)? Explain. Question 2 Recently, the re-appearance of several childhood illness has raised concerns about the immunization program in Nova Scotia. The Minister of Health wishes to estimate the proportion of families in Nova Scotia who do follow the recommended immunization schedule. In a random sample of 110 families from a large Family Practice (doctor’s office with more than one doctor on staff) in Nova Scotia, 104 reported that they follow the recommendation about childhood immunization. Test and CI for One Proportion Sample X N Sample p 95% CI 1 104 110 0.945455 (0.903017, 0.987892) Using the normal approximation. The five statements below are related to a 95% confidence interval for this data. Label each statement true or false. If the statement is false, explain why it is false. a. The Minister of Health is 95% certain that the proportion of the 110 families follow the recommended immunization schedule is between 0.90 and 0.99. b. The Minitab of Health is 95% certain that the proportion of the 110 families who follow the recommended immunization schedule is 0.95. c. Assuming that a normal model can be used, the Minister of Health is 95% certain that the proportion of all families in Nova Scotia who follow the recommended immunization schedule will be between 90% and 99%. d. Assume that a normal model can be used. The Minister of Health is more than 95% certain the proportion of families in Nova Scotia who follow the recommended immunization schedule will be in this range. e. Assuming that a normal model can be used, the Minister of Health is 95% certain that the proportion of all families in Canada who follow the recommended immunization schedule will be between 90% and 99%. Question 3 Each of the three situations below requires a hypothesis test about a population proportion. In each case, state the appropriate null hypothesis (Ho) and alternative hypothesis (Ha) in symbols. For part (a) only, also define the parameter (p). a. A city claims that 75% of all low income housing is 1500 sq. ft. The tenants believe the proportion of housing this size is smaller than the claim, and hire an independent firm to test an appropriate hypothesis. b. To maintain good oral health, the Canadian Dental Association recommends brushing, flossing, regular check-ups, and cleaning by a dentist. Although the cost for preventative dental care can be less than the eventual cost for the treatment of problems caused by neglect, many students simply cannot afford to go to the dentist every year. Past records from the CDA show that 55% of university students visit the dentist on a yearly basis. The Association is interested in whether this proportion has changed. c. A large software company gives job applicants a test of programming ability, and the pass rate for the test has been 80% in the past. A statistical analyst in the company conducts a study using this year’s applicant data to see if there evidence to indicate that the pass rate has increased.