Q. 28 - The Practice of Statistics for AP

Question

The candy machine Suppose a large candy machine has 15% orange candies. Use Figure 7.13 (page 435) to help answer the following questions.

(a) Would you be surprised if a sample of 25 candies from the machine contained 8 orange candies (that's $32\%$orange)? How about 5 orange candies ( orange)? Explain.

(b) Which is more surprising: getting a sample of 25 candies in which $32\%$ are orange or getting a sample of 50 candies in which $32\%$ are orange? Explain.

Step-by-Step Solution

Answer

a. $8$ orange candies: Surprising; $5$ orange candies: Not surprising

b. $32\%$ orange candies in a sample of $50$ is surprising.

Part (a) Step 1: Given Information

A large candy machine has $=15\%$orange candies

Sample candies $=25$

8 orange candies (that's $32\%$ orange)

5 orange candies ( $20\%$orange) $=?$

Part (a) Step 2: Explanation

There are no dots above or below the sample proportion of or $0.32$ in figure $7.13$'s dot plot.

This means that obtaining a proportion of $32$ is extremely improbable, therefore $8$ orange candies are an unexpected result.

The dot plot in figure $7.11$ illustrates that the sample proportion of $20\%$, or $0.20$, has a lot of dots above it, indicating that getting a sample proportion of $20\%$ is extremely possible; thus, $5$ orange candies are not unusual.

Part (b) Step 1: Given Information

A large candy machine has $=15\%$ orange candies

Sample candies $=25$

Either Sample of $25$ candies in which $32\%$ are orange or a sample of $50$ candies in which$32\%$ are orange is surprising ?

Part (b) Step 2: Explanation

The center of this distribution, according to figure $7.13$, is around $0.15.$

However, three-quarters of this proportion, or $0.32$, does not match the $0.15$ population proportion.

It is more odd to receive a sample proportion that is distant from the average for samples with a higher sample size (which contains more information about the population), therefore $32$ percent orange candies out of $50$ candies is more unexpected.