Question

1. 40 university undergraduate students will be randomly selected from those expressing interest to attend an online webinar hosted by a famous author. of the 1,207 undergraduate students who expressed interest, 93 were from the university of michigan. of the 40 randomly selected to attend the webinar, 6 were from the university of michigan. a consulting statistician is concerned that there may have been a selection bias in the choosing of the participants. to investigate how likely it is that at least 6 of the 40 students chosen to attend would have been from the university michigan purely by chance, the statistician ran a simulation. the simulation is described by the following steps: step 1: locate 93 blue and 1,114 red chips. step 2: select 40 chips at random. step 3: record the number of blue chips in the 40 chips that were selected. the results of 1,000 trials of the simulation are shown in the histogram. based on the results of the simulation, is there convincing statistical evidence at the 5% significance level that selecting at least 6 of the 40 students from the university of michigan is unlikely to have occurred by chance alone? a) yes, because 6 appears after the third quartile of simulated values. b) yes, because the expected number of blue chips is not close to 6. c) yes, because the distribution of the trials in the simulation is skewed to the right. d) no, because the simulation suggests that selecting between 0 and 9 students from the university of michigan is likely. e) no, because the simulation suggests that selecting at least 6 of 40 students from the university of michigan would occur about 7.4% of the time purely by chance alone.

Explanation:

Step1: Understand significance level

A significance level of 5% means that if an event occurs less than 5% of the time by chance, we have convincing evidence.

Step2: Analyze simulation results

We need to find the proportion of trials where the number of blue chips (representing University of Michigan students) is at least 6.
Sum the frequencies for 6, 7, 8, 9: \(41 + 24+7 + 2=74\)
The proportion is \(\frac{74}{1000}=0.074 = 7.4\%\)

Answer:

E. No, because the simulation suggests that selecting at least 6 of 40 students from the University of Michigan would occur about 7.4% of the time purely by chance alone.