Exam-Style Question on Significance
A mathematics exam-style question with a worked solution that can be revealed gradually
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.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
If you need to revise the details of the t-test see this presentation.
©1997 - 2020 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/