Probability analysis of soft drink brand identification in taste tests

Drink Probability Experiment

Preface to Study

You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to identify the brand tasted.

You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands. (Hint: if an individual has no ability to distinguish between the two soft drinks, then each brand is equally likely to be selected).

What is the probability that the sample will have between 50% and 60% of the identifications correct?

Each taste has a 50/50 chance that the brand will be identified.

Where between 50% and 60% identifications are correct, there is a 90% probability, with a 10% margin of error.

The probability is 90% that the sample percentage is contained within what symmetrical limits of the population percentage?

We do not know the definition of 'population' here in terms of numbers.

The analysis assumes that infinity is reflected in the randomness of the study's sample population.

The probability that the sample percentage is contained within the symmetrical limits of the population percentage: < or = 100%

Symmetrical limits are understood as 0 to 100, with a probable outcome of a 50/50 chance each taste.

3. What is the probability that the sample percentage of correct identifications is greater than 65%?

Where the population is 200 respondents

And they are asked to take a taste test of one of two available drink brands

Each taste has a 50/50 (50%) chance of identification

The probability that the sample percentage of correct identifications is greater than 65% is: .10 or 10%

200 x 1 taste = 200 tastes

Where 90% of those tastes fall between 50 and 60% =180

It is possible that the remaining 20 respondents might have greater than 65% identification or .1

4. Which is more likely to occur: more than 60% correct identifications in the sample of 200; or more than 55% correct identifications in a sample of 1,000? Explain.

Using the same analysis to describe the comparative probability that one is more likely to occur

Where more than 60% correct identification in a sample of 200