Exam 6: Comparing Two Proportions

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. -Does there appear to be an association between whether one takes Claritin or a placebo and the development of drowsiness in this sample?

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 the p-value for a test of test . versus

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. -Calculate the conditional proportion of trout that developed whirling disease for each species (rainbow or brown): Rainbow: ___ (1) ___ Brown: ___(2) ___

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 we had calculated a 95% confidence interval in question 33 rather than a 90% confidence interval, all else being equal, would the resulting interval be wider, narrower, or the same width?

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. -Use the Theory-Based Inference applet to find a 95% confidence interval for the difference in probability of agreeing with the statement in the study between the two groups (student - non-student). (___(1)___, ___(2)___)

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. -Based on the study design, what is the scope of inference for these results?

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. What is the strength of evidence against observed study results happening by chance alone?

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. -Is a theory-based approach appropriate to test versus ?

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. -State the null and alternative hypotheses.

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. -Which of the following plots would be most appropriate to examine the association between the explanatory and response variables?

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. -Based off of your confidence interval in question 33, what could you say for sure about the p-value for testing versus ?

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. -What does it mean to have 95% confidence in the interval you created in question 40?

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. -Organize these data into a two-way table:

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. -Calculate the relative risk of whirling disease for rainbow trout compared to brown trout in this sample.

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. -What is the value of the statistic and its appropriate notation?

The p-value for a test of two proportions is the probability that the two long-run proportions are equal.

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. -Is a theory-based approach appropriate to evaluate the relationship between whether an individual took aspirin or a placebo and whether an individual suffers a heart attack?

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. -Use the Theory-Based Inference applet to find the p-value for a test of test versus

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. -The study concluded that "in the U.S., a higher percentage of high school students believe controversial issues should be reported without approval of school authorities than high school teachers." Is this conclusion justified?

A simulated null distribution of a difference in sample proportions will be centered at the value of the difference in proportions in the observed data.