Question

The candy machine Suppose a large candy machine has $45\%$orange candies, Use Figures $7.11and7.12$(page 434) 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 ( $20\%$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.

Short answer

(a) Obtaining $8$orange candies is not very surprising,

Obtaining $5$orange candies is surprising.

(b) Getting a sample of $50$candies in which $32\%$are orange candies is more surprising.

Step-by-step solution

Part (a) Step 1: Given Information 

Given in the question that sample of $25$candies from the machine contained $8$orange candies (that's $32\%$orange)? and $5$orange candies ( $20\%$orange).we have to find that which sample would be surprised.

Part (a) Step 2: Explanation 

In the candy machine, the percentage of orange candies is $45$

The dot plot shows that the sample percentage of $32$percent has a lot of dots above it, indicating that getting a sample proportion of $32$percent is quite likely.

As a result, getting $8$orange candies isn't all that surprising.

In the dot plot, the sample percentage of $20\%$ now has no dots above it, indicating that getting a sample proportion of $20\%$is unlikely.

As a result, getting$5$ orange candy is a pleasant surprise.

Part (b) Step 1: Given Information 

Given in the question that a sample of $25$candies in which $32\%$are orange or getting a sample of $50$candies in which $32\%$are orange we have to find Which is more surprising.

Part (b) Step 2:  Explanation 

In the candy machine, the percentage of orange candies is $45\%$

In the dot plots, the centre of the distribution is around $0.45$.

It can be seen that the population proportion of $0.45$is not very close to$32\%$

It is more unusual to achieve a sample proportion that differs from the population proportion for a sample with a greater sample size.

As a result, receiving a sampling of $50$candies, with $32$percent of them being orange candies, is even more shocking.