Question

4.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?

Select one:

a. Yes

b. No

5.Consider the information in Question 4. What is the smallest possible sample size (i.e., number of people taking the blind taste test) needed to insure that the sampling distribution of the proportion is normal?

Select one:

a. 8

b. 10

c. 12

d. 18

e. 20

Answer 1

4. Yes.

Here we assume that "it is true that people can not tell the difference between Coke and Pepsi".

Therefore, the proportion of not tell the difference between Coke and Pepsi is 0.5

The use of the normal distribution as an approximation to the binomial when

Satifying the following two conditions.

i) np >= 5 and ii) n(1 - p) >= 5.

Here n = 15 and p = 0.5

i ) n * p = 15 * 0.5 = 7.5 > 5

and n * (1 - p) = 15 * ( 1 - 0.5) = 15 * 0.5 = 7.5 > 5

Both the conditions are satisfied.

So we can use normal approximation to the binomial distribution.

5) the correct option is b. 10

We want to find n such that

We want to take n such as maximum { n*p = 5, and n* (1 - p) = 5 ) for given p.

Here p = 0.5.

Therefore n* ( 0.5) = 5

therefore n = 5/0.5 = 10

and n*(1-p) = 5

n = 5/( 1-0.5) = 10

therefore n = maximum of {10, 10) = 10

So the conditions of normal approximation to the binomial are satisfied for the minimum value of the sample size is 10.