Chapter 5.1, Problem 23E

(a)

To determine

To explain why this result does not give convincing evidence that more than half of the school’s student recycle.

Explanation of Solution

It does not give convincing evidence that more than half of the school’s student recycle because:

  $55\text{ out of 100}$ students answered “Yes”.

  $\frac{55}{100}=0.55$

In the given dot plot we note that the proportion of $0.55$ has many dots above it.

Thus it is very likely to obtain a proportion of

  $0.55$ when the true proportion is $0.5$ and then there is not sufficient evidence to support the claim that more than half of the school’s student recycle.

(b)

To determine

To explain why this result gives strong evidence that a majority of the school’s students recycle.

Explanation of Solution

This result gives strong evidence that a majority of the school’s students recycle because:

  $\text{63 out of 100}$ students answered “Yes”.

  $\frac{63}{100}=0.63$

In the given dot plot we note that the proportion of $0.63$ has only one dot above it and there are no dots to the right of $0.63$ .

Thus it is very likely to obtain a proportion of

  $0.63$ when the true proportion is $0.5$ and then there is sufficient evidence to support the claim that more than half of the school’s student recycle.

Hence the result.