Questions: A random sample of 100 freshman showed 8 had satisfied the university mathematics requirement and a second random sample of 50 sophomores showed that 12 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 (b) The increased risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is

Solution Steps

To solve this problem, we need to calculate the relative risk and the increased risk based on the given data.

1. Relative Risk: This is the ratio of the probability of an event occurring in the exposed group (sophomores) to the probability of the event occurring in the control group (freshmen).
2. Increased Risk: This is the difference in the probability of the event occurring between the two groups.

1. Calculate the probability of satisfying the requirement for both freshmen and sophomores.
2. Compute the relative risk by dividing the probability for sophomores by the probability for freshmen.
3. Compute the increased risk by subtracting the probability for freshmen from the probability for sophomores.

First, we calculate the probabilities of satisfying the university mathematics requirement for both freshmen and sophomores.

For freshmen: \[ P(\text{freshmen}) = \frac{8}{100} = 0.08 \]

For sophomores: \[ P(\text{sophomores}) = \frac{12}{50} = 0.24 \]

Next, we calculate the relative risk, which is the ratio of the probability for sophomores to the probability for freshmen.

\[ \text{Relative Risk} = \frac{P(\text{Sophomores})}{P(\text{Freshmen})} = \frac{0.24}{0.08} = 3.0 \]

Then, we calculate the increased risk, which is the difference in the probabilities between sophomores and freshmen.

\[ \text{Increased Risk} = P(\text{Sophomores}) - P(\text{Freshmen}) = 0.24 - 0.08 = 0.16 \]

Final Answer