1. Genital human papillomaviruses (HPV) is common among US females and infection with certain types of HPV may lead to cervical cancer, anogenital and oropharyngeal cancer, and anogential warts. In a recent study based on the National Health and Nutrition Examination Surveys (2003-2006), which has a sample size of 4150, prevalence of HPV was estimated for different subpopulation of females according to the various age groups. Age Groups 14-19 20-24 25-29 30-39 40-49 50-59 Total Sample Size (n) 1363 432 403 702 705 545 4150 HPV Prevalence (%) 32.9 53.8 46.8 44.2 42.4 38.8 42.5 a. Suppose that a sample of 9 random women between the ages of 40 and 49 years were drawn from US females. What is the probability that none of them have HPV? b. In the same sample above, what is the probability that at least 1 is HPV infected? c. In the above scenario, would you be justified in approximating the probabilities using the standard normal table? Explain why. d. What is the prevalence of HPV in those who are between 30-59 years old? 2. Hypothetical Study of Alcohol Consumption and Breast Cancer: You conduct a study to determine whether breast cancer in African-American and Hispanic women living in the Chicago area is associated with drinking alcohol. Study Design - With help from the Illinois State Cancer Registry, you identify 250 cases of breast cancer in African-American women and 250 cases in Hispanic women diagnosed in January of this year. Next, you identify 500 African-American and Hispanic women without a history of breast cancer from a list of persons responding to a Chicago area health survey administered in January of this year. Drinking habits during the previous 5 years are compared, and the results are shown below: Alcohol consumed/wk during the previous 5 years (average) Breast Cancer Yes No > 20 ounces 371 235 606 20 ounces or less 129 265 394 500 500 Totals a. What is the joint probability of having breast cancer (D+) and consuming more than 20 ounces of alcohol per week (E+)? b. What would you expect the above joint probability to equal if there was no association between alcohol consumption and breast cancer? 1. Genital human papillomaviruses (HPV) is common among US females and infection with certain types of HPV may lead to cervical cancer, anogenital and oropharyngeal cancer, and anogential warts. In a recent study based on the National Health and Nutrition Examination Surveys (2003-2006), which has a sample size of 4150, prevalence of HPV was estimated for different subpopulation of females according to the various age groups. Age Groups 14-19 20-24 25-29 30-39 40-49 50-59 Total Sample Size (n) 1363 432 403 702 705 545 4150 HPV Prevalence (%) 32.9 53.8 46.8 44.2 42.4 38.8 42.5 a. Suppose that a sample of 9 random women between the ages of 40 and 49 years were drawn from US females. What is the probability that none of them have HPV? Here, X = Number of females out of 9 who has HPV~Binomial( n = 9; p =0.424) P(None of them have HPV) = P(X = 0) 9! 0.4240( 10.424 )90 = 0!( 90 ) ! = 0.0069791 b. In the same sample above, what is the probability that at least 1 is HPV infected? P(At least one have HPV) = 1- P(None have HPV) = 1- 0.0069791 = 0.9930209 c. In the above scenario, would you be justified in approximating the probabilities using the standard normal table? Explain why. In this case, n = 9 and p = 0.424 so we can see that, np = 9*0.424 = 3.816 < 5 Thus the normal approximation is not appropriate. d. What is the prevalence of HPV in those who are between 30-59 years old? Prevalence of HPV in those who are between 30-59 years old = (702*44.2% +705*42.4% + 545*38.8%)/(702+705+545) = 42.04% 2. Hypothetical Study of Alcohol Consumption and Breast Cancer: You conduct a study to determine whether breast cancer in African-American and Hispanic women living in the Chicago area is associated with drinking alcohol. Study Design - With help from the Illinois State Cancer Registry, you identify 250 cases of breast cancer in African-American women and 250 cases in Hispanic women diagnosed in January of this year. Next, you identify 500 African-American and Hispanic women without a history of breast cancer from a list of persons responding to a Chicago area health survey administered in January of this year. Drinking habits during the previous 5 years are compared, and the results are shown below: Alcohol consumed/wk during the previous 5 years (average) Breast Cancer Yes No > 20 ounces 371 235 606 20 ounces or less 129 265 394 500 500 Totals a. What is the joint probability of having breast cancer (D+) and consuming more than 20 ounces of alcohol per week (E+)? P(Breast cancer and consuming more than 20 ounces of alcohol ) =P(D+ and E+) = total number of peop Number of people with Breast cancerconsuming more than 20 ounces of alcohol = 371/1000 = 0.371 b. What would you expect the above joint probability to equal if there was no association between alcohol consumption and breast cancer? Expected probability = P(D+)*P(E+)= 606/1000*500/1000 = 0.303 1. Genital human papillomaviruses (HPV) is common among US females and infection with certain types of HPV may lead to cervical cancer, anogenital and oropharyngeal cancer, and anogential warts. In a recent study based on the National Health and Nutrition Examination Surveys (2003-2006), which has a sample size of 4150, prevalence of HPV was estimated for different subpopulation of females according to the various age groups. Age Groups 14-19 20-24 25-29 30-39 40-49 50-59 Total Sample Size (n) 1363 432 403 702 705 545 4150 HPV Prevalence (%) 32.9 53.8 46.8 44.2 42.4 38.8 42.5 a. Suppose that a sample of 9 random women between the ages of 40 and 49 years were drawn from US females. What is the probability that none of them have HPV? Here, X = Number of females out of 9 who has HPV~Binomial( n = 9; p =0.424) P(None of them have HPV) = P(X = 0) = ( ) ( ) = 0.0069791 b. In the same sample above, what is the probability that at least 1 is HPV infected? P(At least one have HPV) = 1- P(None have HPV) = 1- 0.0069791 = 0.9930209 c. In the above scenario, would you be justified in approximating the probabilities using the standard normal table? Explain why. In this case, n = 9 and p = 0.424 so we can see that, np = 9*0.424 = 3.816 < 5 Thus the normal approximation is not appropriate. d. What is the prevalence of HPV in those who are between 30-59 years old? Prevalence of HPV in those who are between 30-59 years old = (702*44.2% +705*42.4% + 545*38.8%)/(702+705+545) = 42.04% 2. Hypothetical Study of Alcohol Consumption and Breast Cancer: You conduct a study to determine whether breast cancer in African-American and Hispanic women living in the Chicago area is associated with drinking alcohol. Study Design - With help from the Illinois State Cancer Registry, you identify 250 cases of breast cancer in African-American women and 250 cases in Hispanic women diagnosed in January of this year. Next, you identify 500 African-American and Hispanic women without a history of breast cancer from a list of persons responding to a Chicago area health survey administered in January of this year. Drinking habits during the previous 5 years are compared, and the results are shown below: Alcohol consumed/wk during the previous 5 years (average) Breast Cancer Yes No > 20 ounces 371 235 606 20 ounces or less 129 265 394 500 500 Totals a. What is the joint probability of having breast cancer (D+) and consuming more than 20 ounces of alcohol per week (E+)? P(Breast cancer and consuming more than 20 ounces of alcohol ) =P(D+ and E+) = = 371/1000 = 0.371 b. What would you expect the above joint probability to equal if there was no association between alcohol consumption and breast cancer? Expected probability = P(D+)*P(E+)= 606/1000*500/1000 = 0.303 1. Genital human papillomaviruses (HPV) is common among US females and infection with certain types of HPV may lead to cervical cancer, anogenital and oropharyngeal cancer, and anogential warts. In a recent study based on the National Health and Nutrition Examination Surveys (2003-2006), which has a sample size of 4150, prevalence of HPV was estimated for different subpopulation of females according to the various age groups. Age Groups 14-19 20-24 25-29 30-39 40-49 50-59 Total Sample Size (n) 1363 432 403 702 705 545 4150 HPV Prevalence (%) 32.9 53.8 46.8 44.2 42.4 38.8 42.5 a. Suppose that a sample of 9 random women between the ages of 40 and 49 years were drawn from US females. What is the probability that none of them have HPV? Here, X = Number of females out of 9 who has HPV~Binomial( n = 9; p =0.424) P(None of them have HPV) = P(X = 0) 9! 0.4240( 10.424 )90 = 0!( 90 ) ! = 0.0069791 b. In the same sample above, what is the probability that at least 1 is HPV infected? P(At least one have HPV) = 1- P(None have HPV) = 1- 0.0069791 = 0.9930209 c. In the above scenario, would you be justified in approximating the probabilities using the standard normal table? Explain why. In this case, n = 9 and p = 0.424 so we can see that, np = 9*0.424 = 3.816 < 5 Thus the normal approximation is not appropriate. d. What is the prevalence of HPV in those who are between 30-59 years old? Prevalence of HPV in those who are between 30-59 years old = (702*44.2% +705*42.4% + 545*38.8%)/(702+705+545) = 42.04% 2. Hypothetical Study of Alcohol Consumption and Breast Cancer: You conduct a study to determine whether breast cancer in African-American and Hispanic women living in the Chicago area is associated with drinking alcohol. Study Design - With help from the Illinois State Cancer Registry, you identify 250 cases of breast cancer in African-American women and 250 cases in Hispanic women diagnosed in January of this year. Next, you identify 500 African-American and Hispanic women without a history of breast cancer from a list of persons responding to a Chicago area health survey administered in January of this year. Drinking habits during the previous 5 years are compared, and the results are shown below: Alcohol consumed/wk during the previous 5 years (average) Breast Cancer Yes No > 20 ounces 371 235 606 20 ounces or less 129 265 394 500 500 Totals a. What is the joint probability of having breast cancer (D+) and consuming more than 20 ounces of alcohol per week (E+)? P(Breast cancer and consuming more than 20 ounces of alcohol ) =P(D+ and E+) = total number of peop Number of people with Breast cancerconsuming more than 20 ounces of alcohol = 371/1000 = 0.371 b. What would you expect the above joint probability to equal if there was no association between alcohol consumption and breast cancer? Expected probability = P(D+)*P(E+)= 606/1000*500/1000 = 0.303 1. Genital human papillomaviruses (HPV) is common among US females and infection with certain types of HPV may lead to cervical cancer, anogenital and oropharyngeal cancer, and anogential warts. In a recent study based on the National Health and Nutrition Examination Surveys (2003-2006), which has a sample size of 4150, prevalence of HPV was estimated for different subpopulation of females according to the various age groups. Age Groups 14-19 20-24 25-29 30-39 40-49 50-59 Total Sample Size (n) 1363 432 403 702 705 545 4150 HPV Prevalence (%) 32.9 53.8 46.8 44.2 42.4 38.8 42.5 a. Suppose that a sample of 9 random women between the ages of 40 and 49 years were drawn from US females. What is the probability that none of them have HPV? Here, X = Number of females out of 9 who has HPV~Binomial( n = 9; p =0.424) P(None of them have HPV) = P(X = 0) = ( ) ( ) = 0.0069791 b. In the same sample above, what is the probability that at least 1 is HPV infected? P(At least one have HPV) = 1- P(None have HPV) = 1- 0.0069791 = 0.9930209 c. In the above scenario, would you be justified in approximating the probabilities using the standard normal table? Explain why. In this case, n = 9 and p = 0.424 so we can see that, np = 9*0.424 = 3.816 < 5 Thus the normal approximation is not appropriate. d. What is the prevalence of HPV in those who are between 30-59 years old? Prevalence of HPV in those who are between 30-59 years old = (702*44.2% +705*42.4% + 545*38.8%)/(702+705+545) = 42.04% 2. Hypothetical Study of Alcohol Consumption and Breast Cancer: You conduct a study to determine whether breast cancer in African-American and Hispanic women living in the Chicago area is associated with drinking alcohol. Study Design - With help from the Illinois State Cancer Registry, you identify 250 cases of breast cancer in African-American women and 250 cases in Hispanic women diagnosed in January of this year. Next, you identify 500 African-American and Hispanic women without a history of breast cancer from a list of persons responding to a Chicago area health survey administered in January of this year. Drinking habits during the previous 5 years are compared, and the results are shown below: Alcohol consumed/wk during the previous 5 years (average) Breast Cancer Yes No > 20 ounces 371 235 606 20 ounces or less 129 265 394 500 500 Totals a. What is the joint probability of having breast cancer (D+) and consuming more than 20 ounces of alcohol per week (E+)? P(Breast cancer and consuming more than 20 ounces of alcohol ) =P(D+ and E+) = = 371/1000 = 0.371 b. What would you expect the above joint probability to equal if there was no association between alcohol consumption and breast cancer? Expected probability = P(D+)*P(E+)= 606/1000*500/1000 = 0.303