Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means.

This question is incomplete, the complete question is;

Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means.

Is the sampling distribution of the difference in sample means approximately normal?

a) Yes, because Alicia selected a random sample

b) Yes, because for each brand it is reasonable to assume that the population size is greater than ten times its sample size.

c) Yes, because the size of each sample is at least 30

d) No, because the distribution of Brand A shoes has outliers

e) No, because the shape of the population distribution is unknown.

the sampling distribution of  the difference in sample means is approximately normal because the size of each sample is al least 30

Option (c) Yes, because the size of each sample is at least 30 ) is the correct answer.

Step-by-step explanation:

Given the data in the question;

sample size of brand A shoes = 40

sample size of brand B shoes = 33

As we can notice,

= 40 > 30

= 33 > 30

Hence, we consider both samples to be large.

Therefore, the sampling distribution of  the difference in sample means is approximately normal because the size of each sample is al least 30.

Option (c) Yes, because the size of each sample is at least 30 ) is the correct answer.