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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 25candies from the machine contained 8orange candies (that's 32%orange)? How about 5orange candies ( 20%orange)? Explain.

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

Short Answer

Expert verified

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

Obtaining 5orange candies is surprising.

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

Step by step solution

01

Part (a) Step 1: Given Information 

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

02

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 32percent has a lot of dots above it, indicating that getting a sample proportion of 32percent is quite likely.

As a result, getting 8orange 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, getting5 orange candy is a pleasant surprise.

03

Part (b) Step 1: Given Information 

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

04

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 0.45is not very close to32%

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 50candies, with 32percent of them being orange candies, is even more shocking.

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