Chapter 5.1, Problem 24E

(a)

To determine

To explain why this result does not give convincing evidence that more than half of the school’s student brush their teeth with the water off.

Explanation of Solution

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

  $\text{27 out of 60}$ students answered “No”.

  $\frac{27}{60}=0.45$

In the given dot plot we note that the proportion of $0.45$ has many dots above it.

Thus it is very likely to obtain a proportion of $0.45$ 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 brush their teeth with the water off.

(b)

To determine

To explain why this result gives strong evidence that fewer than $50\%$ of the school’s student brush their teeth with the water off.

Explanation of Solution

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

  $\text{18 out of 60}$ students answered “Yes”.

  $\frac{18}{60}=0.3$

In the given dot plot we note that the proportion of $0.3$ has no dot above it and there are no dots to the leftof $0.3$ .

Thus it is very likely to obtain a proportion of $0.3$ 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 brush their teeth with the water off.

Hence the result.