Question

a market analyst creates a taste test to be conducted in a local shopping mall. the experiment asks 500 participants to select which of 2 soft drinks they prefer. the drinks are the same color and in similar cups. participants record their preferred drink on a ballot and place it in a box. they are not told which drink they select. based on national sales data, the analyst expects 65% of participants to select soft drink b. of the 500 participants, 72% select soft drink b.
what can you conclude about this experiment?
select all that apply.
the experiment is not binomial because later participants know which drink earlier ones preferred.
the analyst expects 325 participants to select soft drink b.
the experiment is binomial because there are 2 choices, 500 trials, and each participant is an independent trial.
there are 140 participants that select soft drink a.
the analyst expects 275 participants to select soft drink a.
the national sales data are accurate in predicting sales of soft drink b.

Explanation:

Step1: Calculate expected number of participants for Soft Drink B

The analyst expects 65% of 500 participants to select Soft Drink B. So, $500\times0.65 = 325$.

Step2: Calculate number of participants for Soft Drink A

Since 72% of 500 participants actually select Soft Drink B, the number of participants who select Soft Drink B is $500\times0.72=360$. Then the number of participants who select Soft Drink A is $500 - 360=140$.

Step3: Check binomial - experiment conditions

There are 2 choices (Soft Drink A or Soft Drink B), 500 independent trials (each participant's choice is independent of others as they are not told which drink they select), so it is a binomial experiment. Also, there is no indication that later participants know which drink earlier ones preferred. And we cannot conclude the accuracy of national - sales data just from this experiment.

Answer:

The analyst expects 325 participants to select Soft Drink B.
The experiment is binomial because there are 2 choices, 500 trials, and each participant is an independent trial.
There are 140 participants that select Soft Drink A.