Exam 6: Comparing Two Proportions

To investigate biases against women in personnel decisions, psychologists performed a randomized experiment on 50 male bank supervisors attending a management institute who volunteered for the study. The supervisors were asked to make a decision on whether to promote a hypothetical applicant based on a personnel file. For 26 of them, the application file described a female candidate; for the others it described a male. The files were identical in all other respects. Results on the promotion decisions for the two groups are shown below. -What is the alternative hypothesis, in words?

Hepatitis C is a blood-born viral infection that causes liver inflammation and infection that, over time, can lead to liver disease. There is no vaccine against this strain of hepatitis, so preventive measures are the only management techniques. One of the ways hepatitis can be transmitted is by use of improperly sterilized tattoo equipment or contaminated dyes, which in turn has led to more stringent sterilization requirements for commercial tattoo parlors. Researchers at the University of Texas Southwestern Medical Center examined the medical records of 113 patients who had a tattoo to see whether these sterilization requirements at commercial parlors are reducing the proportion of hepatitis C among those with tattoos, compared to those who get tattoos elsewhere. Data are summarized in the following table. -Is a theory-based approach appropriate to evaluate the relationship between the incidence of hepatitis C and the type of tattoo parlor?

The article "Freedom of What?" (Associated Press, February 1, 2005) described a study in which high school students and high school teachers were asked whether they agreed with the following statement: "Students should be allowed to report controversial issues in their student newspapers without the approval of school authorities." Researchers hypothesized that the long-run proportion of high school teachers who would agree with the statement would differ from the long-run proportion of high school students who would agree. Two random samples - 8,000 high school teachers and 10,000 high school students - were selected from high schools in the U.S. It was reported that 39% of the teachers surveyed and 58% of the students surveyed agreed with the statement. -Fill in the table below with the inputs to the Two Proportion applet to conduct a simulation of the null hypothesis.

The Women's Health Study included 39,876 female health professionals aged 45 years and older who were followed for an average of 10 years (Ridker et al., 2005). At the beginning of the study, participants were randomly assigned to take either a daily low-dose aspirin or a daily placebo pill for the duration of the study. At the end of the study, researchers measured the number of participants that suffered from a heart attack during the study. Data are summarized in the following table. -Use the Theory-Based Inference applet to find a 90% confidence interval for the difference in probability of suffering a heart attack between the two groups (aspirin - placebo). (___(1)___, ___(2)___)

A 2003 study reported in the Journal of Consumer Affairs examined how well consumers protect themselves from identity theft. The study surveyed a random sample of 61 college students and 59 non-students, and asked each participant, "Have you used personal information (such as birth date, pet name, etc.) when creating a password?" For the students, 22 agreed with this statement, while 30 of the non-students agreed. -Calculate the difference between the proportion of college students that agreed with the statement and the proportion of nonstudents that agreed with the statement in the study (student - non-student).

Hepatitis C is a blood-born viral infection that causes liver inflammation and infection that, over time, can lead to liver disease. There is no vaccine against this strain of hepatitis, so preventive measures are the only management techniques. One of the ways hepatitis can be transmitted is by use of improperly sterilized tattoo equipment or contaminated dyes, which in turn has led to more stringent sterilization requirements for commercial tattoo parlors. Researchers at the University of Texas Southwestern Medical Center examined the medical records of 113 patients who had a tattoo to see whether these sterilization requirements at commercial parlors are reducing the proportion of hepatitis C among those with tattoos, compared to those who get tattoos elsewhere. Data are summarized in the following table. -Use the Theory-Based Inference applet to find a 95% confidence interval for the difference in probability of developing hepatitis C between the two types of parlors (commercial - elsewhere). (___(1)___, ___(2)___)

A 2003 study reported in the Journal of Consumer Affairs examined how well consumers protect themselves from identity theft. The study surveyed a random sample of 61 college students and 59 non-students, and asked each participant, "Have you used personal information (such as birth date, pet name, etc.) when creating a password?" For the students, 22 agreed with this statement, while 30 of the non-students agreed. -If we increased the confidence level from 95% to 99%, all else remaining the same, the width of the confidence interval would

A Gallup poll headline from April 25, 2013, reads "In U.S., Women Veterans Rate Lives Better Than Men". In a random sample of 900 female veterans interviewed, 459 rated their lives as "thriving." Only 693 male veterans rated their lives as "thriving" in a random sample of size 1,650. -Organize these data into a two-way table:

To investigate biases against women in personnel decisions, psychologists performed a randomized experiment on 50 male bank supervisors attending a management institute who volunteered for the study. The supervisors were asked to make a decision on whether to promote a hypothetical applicant based on a personnel file. For 26 of them, the application file described a female candidate; for the others it described a male. The files were identical in all other respects. Results on the promotion decisions for the two groups are shown below. -The standardized statistic for this study is 2.59. How would you interpret this value?

The article "Freedom of What?" (Associated Press, February 1, 2005) described a study in which high school students and high school teachers were asked whether they agreed with the following statement: "Students should be allowed to report controversial issues in their student newspapers without the approval of school authorities." Researchers hypothesized that the long-run proportion of high school teachers who would agree with the statement would differ from the long-run proportion of high school students who would agree. Two random samples - 8,000 high school teachers and 10,000 high school students - were selected from high schools in the U.S. It was reported that 39% of the teachers surveyed and 58% of the students surveyed agreed with the statement. -A simulated null distribution of 1,000 differences in proportions created by using the Two Proportion applet is shown below. Use the 2SD method to find a 95% confidence interval for the difference in long-run proportion who would agree with the statement between Students and Teachers (Students - Teachers). (____(1)____, ____(2)____)

A Gallup poll headline from April 25, 2013, reads "In U.S., Women Veterans Rate Lives Better Than Men". In a random sample of 900 female veterans interviewed, 459 rated their lives as "thriving." Only 693 male veterans rated their lives as "thriving" in a random sample of size 1,650. -For each sample (females and males), calculate the sample proportion who rated their lives as "thriving." Females: ________ Males:________

The Women's Health Study included 39,876 female health professionals aged 45 years and older who were followed for an average of 10 years (Ridker et al., 2005). At the beginning of the study, participants were randomly assigned to take either a daily low-dose aspirin or a daily placebo pill for the duration of the study. At the end of the study, researchers measured the number of participants that suffered from a heart attack during the study. Data are summarized in the following table. -If our sample size had been 10,000 rather than 39,876, all else being equal, would the 90% confidence interval be wider, narrower, or the same width as the one found in question 33?

Whirling disease is a deadly disease that affects trout in Montana rivers. In a follow-up to a 2006 study conducted by the Montana Department of Fish, Wildlife and Parks (FWP), researchers sought to determine if the proportion of trout afflicted by whirling disease in the Gallatin river differs between rainbow trout and brown trout. To test this theory, researchers collected a representative sample of 527 rainbow trout and 459 brown trout. Of the 527 rainbow trout collected, 120 had developed whirling disease; of the 459 brown trout collected, 74 had developed whirling disease. -Based on the relative risk found in question 6, does it appear that whether a trout develops whirling disease is associated with the species of trout (rainbow or brown)?

To investigate biases against women in personnel decisions, psychologists performed a randomized experiment on 50 male bank supervisors attending a management institute who volunteered for the study. The supervisors were asked to make a decision on whether to promote a hypothetical applicant based on a personnel file. For 26 of them, the application file described a female candidate; for the others it described a male. The files were identical in all other respects. Results on the promotion decisions for the two groups are shown below. -The standardized statistic for this study is 2.59, and the p-value is 0.009. State a conclusion of the test in context of the problem.

The article "Freedom of What?" (Associated Press, February 1, 2005) described a study in which high school students and high school teachers were asked whether they agreed with the following statement: "Students should be allowed to report controversial issues in their student newspapers without the approval of school authorities." Researchers hypothesized that the long-run proportion of high school teachers who would agree with the statement would differ from the long-run proportion of high school students who would agree. Two random samples - 8,000 high school teachers and 10,000 high school students - were selected from high schools in the U.S. It was reported that 39% of the teachers surveyed and 58% of the students surveyed agreed with the statement. -Describe how you could use cards to simulate a single sample statistic in the null distribution.

Whirling disease is a deadly disease that affects trout in Montana rivers. In a follow-up to a 2006 study conducted by the Montana Department of Fish, Wildlife and Parks (FWP), researchers sought to determine if the proportion of trout afflicted by whirling disease in the Gallatin river differs between rainbow trout and brown trout. To test this theory, researchers collected a representative sample of 527 rainbow trout and 459 brown trout. Of the 527 rainbow trout collected, 120 had developed whirling disease; of the 459 brown trout collected, 74 had developed whirling disease. -Identify the explanatory and response variables, and their types by filling in the blanks below: The type of trout (rainbow or brown) is the ___(1)___ (explanatory/response) variable and it is ___(2)___ (categorical/quantitative). Whether or not the trout developed whirling disease is the ___(3)___ (explanatory/response) variable and it is ___(4)___ (categorical/quantitative).

The Women's Health Study included 39,876 female health professionals aged 45 years and older who were followed for an average of 10 years (Ridker et al., 2005). At the beginning of the study, participants were randomly assigned to take either a daily low-dose aspirin or a daily placebo pill for the duration of the study. At the end of the study, researchers measured the number of participants that suffered from a heart attack during the study. Data are summarized in the following table. -Calculate the relative risk of heart attack for the low-dose aspirin group compared to the placebo group.

Whirling disease is a deadly disease that affects trout in Montana rivers. In a follow-up to a 2006 study conducted by the Montana Department of Fish, Wildlife and Parks (FWP), researchers sought to determine if the proportion of trout afflicted by whirling disease in the Gallatin river differs between rainbow trout and brown trout. To test this theory, researchers collected a representative sample of 527 rainbow trout and 459 brown trout. Of the 527 rainbow trout collected, 120 had developed whirling disease; of the 459 brown trout collected, 74 had developed whirling disease. -Based on the conditional proportions found in question 4, does it appear that whether a trout develops whirling disease is associated with the species of trout (rainbow or brown)?

To investigate biases against women in personnel decisions, psychologists performed a randomized experiment on 50 male bank supervisors attending a management institute who volunteered for the study. The supervisors were asked to make a decision on whether to promote a hypothetical applicant based on a personnel file. For 26 of them, the application file described a female candidate; for the others it described a male. The files were identical in all other respects. Results on the promotion decisions for the two groups are shown below. -What is the value of the statistic and its appropriate notation?

An advertisement for Claritin, a drug for seasonal nasal allergies, made this claim: "Clear relief without drowsiness. In studies, the incidence of drowsiness was similar to placebo" (Time, February 6, 1995, p. 43). The advertisement also reported that 8% of the 1,926 Claritin takers and 6% of the 2,545 placebo takers reported drowsiness as a side effect. -Calculate the relative risk of drowsiness for Claritin users compared to placebo.