Question

question 39 (1 point) saved exhibit 7 - 11 a student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years. randomization part of study? retro. observational pro. observational experiment yes no 7 53 28 62 35 115 refer to exhibit 7 - 11. define the events e = {the study was an experiment} and u = {the study used randomization}. are the events e and u independent? yes no cant tell need more information to determine this. question 40 (1 point) saved

Explanation:

Step1: Recall the definition of independent events

Two events E and U are independent if \(P(E\cap U)=P(E)\times P(U)\). We need to calculate the probabilities from the given frequency - table data.
The total number of studies \(n = 53 + 7+62 + 28+115 + 35=300\).
\(P(E)=\frac{7 + 28+35}{300}=\frac{70}{300}=\frac{7}{30}\)
\(P(U)=\frac{35 + 7}{300}=\frac{42}{300}=\frac{7}{50}\)
\(P(E\cap U)=\frac{35}{300}=\frac{7}{60}\)

Step2: Check the independence condition

\(P(E)\times P(U)=\frac{7}{30}\times\frac{7}{50}=\frac{49}{1500}
eq\frac{7}{60}=\frac{175}{1500}\)

Answer:

No