Question

1. In a study at West Virginia University Hospital, researchers investigated smoking behavior of cancer patients to create a program to help patients stop smoking. They published the results in Smoking Behaviors Among Cancer Survivors (January 2018, Journal of Oncology Practice). In this study, the researchers sent a 22-item survey to 1286 cancer patients. They collected demographic information (age, sex, ethnicity, zip code, level of education), clinical and smoking history, and information about quitting smoking.

Of the 1286 patients who were mailed surveys, 257 patients responded. For various reasons, researchers used only 231 of the completed surveys. 39 out of 120 female cancer patients reported being past smokers, and 66 out of 111 male cancer patients reported being past smokers. Calculate the difference between the corresponding sample proportions ^p1−^p2 (female minus male). Round the answer to 4 decimal places.

2. In 2014, students in an advanced Statistics course at UC Berkeley conducted an anonymous survey about use of cognition-enhancing drugs among college males. One survey group of males included members from a fraternity, and the other survey group of males included no fraternity members.

The standard error formula for the difference between sample proportions is

Calculate the standard error for a survey comparing proportions of cognition-enhancing drug use of fraternity members to non-fraternity members, where p1 = 0.3, n1 = 142, p2 = 0.25, n2 = 97. Round all calculations to the thousandth decimal place.

Answer 1

1.

n1 = number of female = 120

x1 = number of female cancer patients = 39

n2 = number of male = 111

x2 = number of male cancer patients = 66

2. The standard error of proportions:

Standard error of difference of proportions = 0.058