Question

Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue.

1) Would you expect using bags of Milk Chocolate M&M's labeled as "Large" size, which contain more candies than the "Medium" size bags, to result in a larger or smaller standard error?

2) For which sample sizes (Fun-Size with 20, Vending Machine with 55, or Medium with 415) would the Central Limit Theorem apply?

Answer 1

1) The bag labeled "Large" will have smaller standard error and the bag labeled "Medium" will result in larger standard error. This is because, according to Central Limit Theorem, standard error = , where n is the sample size and hence, standard error decreases as n increases.

2) Central Limit Theorem can be applied for sample sizes 30 and above. Therefore, Vending Machine with 55 and Medium with 415 are the sample to which Central Limit Theorem can be applied.