Question

80% of Americans start the day with a cereal breakfast. Based on this information, determine if the following statement is true or false. "The sampling distribution of the proportions of Americans who start the day with a cereal breakfast in random samples of size 40 is right skewed."

Answer 1

Answer:

FALSE

Step-by-step explanation:

A binomial distribution is a data distribution where there are only 2 possible outcomes A or B.

If probability p is assigned to outcome A, and  probability q is assigned to outcome B, then q = 1 - p.

In a binomial distribution, the mean is np, where n is the size of the sample, and the skewness is

$\frac{1-2p}{\sqrt{npq}}$

As you can see, if p is different to 0.5 a binomial distribution is always skewed, and the skewness is independent of the sample size. Moreover, the sign of the skew only depends on the sign of 1 -2p

In this problem, we could have named:

Event A : The interviewed answered “YES” to the question “Do you start the day with a cereal breakfast?”

Event B: The interviewed answered “NO” to the question “Do you start the day with a cereal breakfast?”

In this case p = 0.8 and the skewness would be negative, so the distribution would be left skewed.