Question

Assume that it is true that people can not tell the difference between Coke and Pepsi. If a sample of 15 people participated in a blind taste test, can we assume that the sampling distribution of the proportion of people that correctly chose Pepsi is normal

Answer 1

Answer:

No

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they can tell the difference between Coke and pepsi, or they cannot. The probability that a person has o telling the difference between Coke and pepsi is independent from each other. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to the normal distribution if

$np \geq 10$

and

$n(1-p)\geq 10$

In this problem, we have that:

$n = 15$

First condition

$np \geq 10$

$15p \geq 10$

$p \geq \frac{10}{15}$

$p \geq \frac{2}{3}$

Second condition

$n(1-p) \geq 10$

$15(1-p) \geq 10$

$15 - 15p \geq 10$

$-15p \geq -5$

Multiplying by -1

$15p \leq 5$

$p \leq \frac{1}{3}$

p cannot be at the at the same time greather than 2/3 and lesser than 1/3. So we cannot assume  that the sampling distribution of the proportion of people that correctly chose Pepsi is normal.