Exam 18: Comparing Two Proportions

A phytologist is worried that a large proportion of the algae found in nearby water sources is cyanobacteria. In particular, he obtains a simple random sample of 50 algae from a local river and an independent simple random sample of 75 algae from the local coastline. He finds that 22 algae in the river sample and 66 algae in the coastline sample are cyanobacteria. He considers the river to act as a control group. Let p₁ and p₂ represent the proportion of cyanobacteria in riparian (i.e., river) and coastal populations, respectively. Is there evidence that the proportion of cyanobacteria is higher in coastal samples than in riparian samples? To determine this, you test the following hypotheses: H₀:p₁ = p₂, H_a:p₁ < p₂ ​ Using technology, what is the value of the z test statistic for testing these hypotheses?

A pioneer study randomly assigned pregnant women to either a daily multivitamin supplement (including folic acid) or a placebo. In the 2104 pregnancies in the women taking the vitamin regimen, there were 28 cases of congenital malformation. In the 2052 pregnancies in the women taking the placebo, 47 cases of congenital malformation were recorded. What is the relative risk reduction, RRR, in congenital malformation when taking a multivitamin supplement compared with taking a placebo?

A survey finds that 13 among a simple random sample of 184 young children have some food allergy, compared with 4 out of 163 adults. We want to compute a 90% plus four confidence interval for P_Childre¯ P_Adults . What is the plus four estimate for the proportion of young adults who have a food allergy?

When using the plus four confidence interval for the difference p₁ - p₂, what do we add?

Could cancer cells be selectively targeted by using antibodies recognizing a tumor-specific protein marker? Researchers grafted human cancerous cells onto 20 healthy adult mice and then randomly assigned 10 of these mice to be treated with tumor-specific antibodies. They found that only 1 of the 10 mice treated with antibodies developed metastases (i.e., new cancer growths), whereas all 10 of the 10 mice in the control group developed metastases. Call (1) the treatment population (injected with antibodies) and (2) the reference population (untreated controls). The relative risk, RR, in metastases development when treated with tumor-specific antigens compared with no treatment is ______________.

A phytologist is worried that a large proportion of the algae found in nearby water sources is cyanobacteria. In particular, he obtains a simple random sample of 50 algae from a local river and an independent simple random sample of 75 algae from the local coastline. He finds that 22 algae in the river sample and 66 algae in the coastline sample are cyanobacteria. He considers the river to act as a control group. Let p₁ and p₂ represent the proportion of cyanobacteria in riparian (i.e., river) and coastal populations, respectively. What is the odds ratio for coastal to riparian environments of algae being cyanobacteria?

Could cancer cells be selectively targeted by using antibodies recognizing a tumor-specific protein marker? Researchers grafted human cancerous cells onto 20 healthy adult mice and then randomly assigned 10 of these mice to be treated with tumor-specific antibodies. They found that only 1 of the 10 mice treated with antibodies developed metastases (i.e., new cancer growths), whereas all 10 of the 10 mice in the control group developed metastases. Call (1) the treatment population (injected with antibodies) and (2) the reference population (untreated controls). The absolute risk reduction, ARR, in metastases development when treated with tumor-specific antigens compared with no treatment is ______________.