4.18 Hypothesis testing: means, proportions, correlation and errorsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 4.18 Hypothesis testing: means, proportions, correlation and errors

1. A machine is set to fill bags of sugar with a mean mass of $500$ g. The mass of a bag is normally distributed with a known standard deviation of $8$ g. An inspector suspects that the machine is under-filling the bags. She takes a random sample of $36$ bags, which has a mean mass of $497.4$ g, and tests the claim at the $5\%$ significance level.
   State the conclusion of the test, giving a reason for your answer.2 marks
2. A trainer records the $100$ m sprint times of $8$ athletes before and after a training programme. The differences in time, in seconds, calculated as before minus after, are $0.12,\ 0.05,\ -0.03,\ 0.20,\ 0.08,\ 0.15,\ 0.02,\ 0.10$. The differences are normally distributed. The trainer tests, at the $5\%$ significance level, whether the programme reduces the mean sprint time. Let $\mu_d$ be the population mean difference. Use your GDC where helpful.
   State the conclusion of the test in context, giving a reason for your answer.2 marks
3. A manufacturer claims that $30\%$ of its customers choose the premium model of a phone. A retailer believes that the proportion is higher. She asks $25$ randomly chosen customers and finds that $12$ of them choose the premium model. She tests the manufacturer's claim at the $5\%$ significance level.
   Let $p$ be the proportion of customers who choose the premium model. Write down the null and alternative hypotheses, and state the distribution of $X$, the number of customers in the sample who choose the premium model, if the null hypothesis is true.3 marks