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Exam-Style Question on Significance

A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 443. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

The 2nd Rutherford American Scouts joined the 37th Wolverhampton British Scouts for an International Camp. Skipper Jones is interested to see if the mean height of American Scouts, \( \mu_1\), is the same as the mean height of British Scouts, \( \mu_2\). The information is recorded in the following table.

American Scout height (cm) 147 153 151 142 155 149 154 156 143 152 149 158      
British Scout height (cm) 142 146 155 145 149 148 152 143 147 150 149 154 150 144 146

At the 10% level of significance, a t-test was used to compare the means of the two groups. The data is assumed to be normally distributed and the standard deviations are equal between the two groups.

(a) State the null hypothesis.

(b) State the alternative hypothesis.

(c) Calculate the p-value for this test.

(d) State, giving a reason, whether Skipper Jones should accept the null hypothesis.

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If you need to revise the details of the t-test see this presentation.

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