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Recycling Do most teens recycle? To find out, an AP Statistics class asked an SRS of 100 students at their school whether they regularly recycle. How many students in the sample would need to say 鈥淵es鈥 to provide convincing evidence that more than half of the students at the school recycle? The Fathom dot plot below shows the results of taking 200 SRSs of 100 students from a population in which the true proportion who recycle is 0.50.

(a) Suppose 55 students in the class鈥檚 sample say 鈥淵es.鈥 Explain why this result does not give convincing evidence that more than half of the school鈥檚 students recycle.

(b) Suppose 63 students in the class鈥檚 sample say 鈥淵es.鈥 Explain why this result gives strong evidence that a majority of the school鈥檚 students recycle.

Short Answer

Expert verified

Part (a) There isn't enough information to back up the assertion that more than half of the students at the school recycle.

Part (b) There is enough information to support the allegation that more than half of the students at the school recycle.

Step by step solution

01

Part (a) Step 1. Given Information 

n=100 SRS size The number of pupils who claimed they recycle is 55

We must decide whether there is persuasive evidence that more than half of the pupils at the school would indicate they recycle regularly using the Fathom dot plot, which displays the results of taking 200 SRSs of 100 students from a population in which the genuine proportion who recycle is 0.50

02

Part (a) Step 2. Concept Used 

A simulation is a model of random behaviour that is usually carried out with random numbers.

03

Part (a) Step 3. Explanation     

It is insufficient proof that more than half of the students at the school recycle because: "Yes" was replied by 55 out of 100 pupils. 55100=0.55

We can see that the proportion of 0.55has a lot of dots above it in the dot plot. As a result, a proportion of 0.55 is quite likely to be obtained when the genuine proportion is 0.5, and there is insufficient evidence to support the assertion that more than half of the school's students recycle.

04

Part (b) Step 1. Explanation  

Because 63 out of 100 students answered "Yes," this statistic strongly suggests that the majority of the school's students recycle 63100=0.63

We can see that the proportion of 0.63 has only one dot above it and no dots to the right of it in the supplied dot plot. Thus, while the genuine proportion is 0.5, a proportion of 0.63 is quite likely to be obtained, and there is adequate evidence to support the assertion that more than half of the school's students recycle. As a result, the outcome.

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