4.11 Hypothesis testing: chi-squared and t-testsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 4.11 Hypothesis testing: chi-squared and t-tests

1. One hundred and fifty students in Year $10$ and Year $11$ were each asked how they usually travel to school. Year $10$ (75 students): walk $20$, bus $30$, car $25$. Year $11$ (75 students): walk $30$, bus $25$, car $20$. A $\chi^2$ test for independence is to be carried out between year group and method of travel.
   Use your GDC to find the $p$-value of the test, and state your conclusion at the $5\%$ significance level.2 marks
2. A café sells four desserts. The manager claims that customers choose the four desserts equally often. In one week, $200$ customers chose cheesecake $68$, brownie $52$, sorbet $44$ and tart $36$ times. A $\chi^2$ goodness of fit test is used to test the claim.
   Write down the null and alternative hypotheses, and the number of degrees of freedom.2 marks
3. A teacher compares the scores of two classes in the same test. Class A has $12$ students with mean score $68.4$ and sample standard deviation $7.2$. Class B has $10$ students with mean score $62.1$ and sample standard deviation $8.1$. The scores in both classes are normally distributed with equal variances. Use a pooled two-sample $t$-test on your GDC.
   Test, at the $5\%$ significance level, whether the mean score of class A is greater than that of class B. State the hypotheses, the $p$-value and your conclusion.3 marks