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Question id: 205. This question is similar to one that appeared in an IB Studies paper in 2015. The use of a calculator is allowed.

### Significance

A survey was conducted asking people's opinions on whether mouthwash should be used before or after brushing teeth. The results are shown as follows.

 Age below 18 Age 18 to 30 Age over 30 Total Before 28 29 33 90 After 24 21 15 60 Total 52 50 48 150

A $$\chi ^2$$ test at the 1% significance level was conducted.

(a) State $$H_0$$, the null hypothesis for the test;

(b) State $$H_1$$, the alternative hypothesis for the test.

(c) Write down the number of degrees of freedom.

(d) Find the expected frequency of people between the age 18 to 30 who believe that mouthwash should be used before brushing.

(e) Find the $$\chi ^2$$ statistic;

(f) Find the associated p-value for the test.

(g) Determine, giving a reason, whether $$H_0$$ should be accepted.

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