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We need to find out the reason for the sample result ($27$of the $60$students said "Yes") does not give convincing evidence that fewer than half of the school's students brush their teeth with the water off.

As we know that $27$out of $60$students who answered "yes"

So, $\frac{27}{60}=0.45$

And We can see that there are many dots above $0.45$in the dotplot, indicating that obtaining a proportion of $0.45$who say "Yes" is quite likely.

Because the sample result is likely to occur, this means that there is no persuasive evidence that fewer than half of the school's children brush their teeth with the water turned off.

We need to find out the reason for the result that would give convincing evidence that fewer than $50\%$of the school's students brush their teeth with the water off.

As we know that $18$out of $60$students who answered "yes"

So,$\frac{18}{60}=0.3$

And, We can see that there are no dots above $0.30$or to the left of $0.30$in the dotplot, indicating that obtaining a proportion of $0.30$who respond "Yes" is extremely unlikely.

Because the sample result is exceedingly improbable to occur, this means that there is solid evidence that fewer than half ($50\%$) of the school's kids clean their teeth with the water turned off.