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Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60students at their school if they usually brush with the water off. In the sample, 27students said "Yes." The dotplot shows the results of taking 200SRSS of 60students from a population in which the true proportion who brush with the water off is 0.50.

a. Explain why the sample result (27of the 60students said "Yes") does not give convincing evidence that fewer than half of the school's students brush their teeth with the water off.

b. Suppose instead that 18of the 60students in the class's sample had said "Yes." Explain why this result would give convincing evidence that fewer than 50%of the school's students brush their teeth with the water off.

Short Answer

Expert verified

(a) In the graph, there are a lot of dots above 0.45of dotplot.

(b) In the dotplot, there are no dots above 0.30or to its left.

Step by step solution

01

Part (a) Step 1: Given information

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

02

Part (a) Step 2: Explanation

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

So, 2760=0.45

And We can see that there are many dots above 0.45in the dotplot, indicating that obtaining a proportion of 0.45who 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.

03

Part (b) Step 1: Given information

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.

04

Part (b) Step 2: Explanation

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

So,1860=0.3

And, We can see that there are no dots above 0.30or to the left of 0.30in the dotplot, indicating that obtaining a proportion of 0.30who 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.

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