Chapter 7.2, Problem 27E

(a)

To determine

Whether it is surprising or not if a sample of 25 candies from the machine contained 8 orange candies or 5 orange candies.

Answer to Problem 27E

It is not surprising if the machine contains 8 orange candies and it is very surprising if the machine contains 5 orange candies.

Explanation of Solution

Given information:

Percent of orange candies in the candy machine = 45%

The sample proportion of 32% contains a lot of dots above it in the dotplot; which means getting a sample proportion of 32% is very likely.

So, obtaining 8 orange candies is not very surprising.

Now, the sample proportion of 20% does not contain any dots above it in the dotplot; which means getting a sample proportion of 20% is not likely.

Thus, obtaining 5 orange candies is surprising.

Hence, it is not surprising if the machine contains 8 orange candies and it is very surprising if the machine contains 5 orange candies.

(b)

To determine

Whether getting a sample of 25 candies in which 32% are orange is more surprising or getting a sample of 50 candies in which 32% are orange.

Answer to Problem 27E

It is more surprising to get a sample of 50 candies in which 32% are orange candies.

Explanation of Solution

Given information:

Percent of orange candies in the candy machine = 45%

The center of the distribution is roughly at about 0.45 in the dotplots.

It is seen that 32% is not very close to the population proportion of 0.45.

Know that to obtain a sample proportion far from the population proportion for sample which has a larger sample size is more unusual.

Hence, getting a sample of 50 candies in which 32% are orange candies is more surprising.