Question

A random sample of 100 freshman showed 5 had satisfed the university mathematics requirement and a second random sample of 50 sophomores showed that 10 had satisfied the university mathematics requirement. Enter answers below rounded to three decimal places. (a) The relative risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is 4 (b) The increased risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is

Answer 1

Answer:

Detailed step wise solution is given below:

Answer 2

(a) The relative risk is $4$.

(b) The increased risk is $3$.

Random Sampling:

In Statistics sampling is a method or process of selecting the subset of the population to form statistical interferences.

The basic feature or characteristic of probability sampling is that the choice of observations must occur in a ‘random’ way such that they do not differ in any significant way from observations, which are not sampled.

Here are the given information we will consider in the table

Gum disease      Yes No Total

Sophomores       10 40    50

Freshmen       5 95    100

Total               15 135    150

a) To determine the relative risk

$Relative \ risk=\frac{Risk \ for \ sophomores }{Risk \ for \ fisherman} \\=\frac{10/50}{5/100} \\=\frac{0.2}{0.05} \\=4$

b) Now, to give the increased risk

$Increased \ risk=relative \ risk-1\\=4-1\\=3$

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