Hypothesis tests for correlationAQA A-Level Maths: Mind map

Exam questions on Hypothesis tests for correlation

1. A teacher records the number of hours $h$ that each of $12$ students spent revising and the student's test score $s$. The product moment correlation coefficient for the sample is $r=0.62$. The teacher tests, at the $5\%$ significance level, whether there is positive correlation between hours revising and test score in the population. For a sample of size $12$, the one-tailed $5\%$ critical value of the product moment correlation coefficient is $0.4973$.
   A student says, 'The test shows that revising for more hours causes higher scores.' Explain why this conclusion is not justified.2 marks
2. A researcher takes a random sample of $10$ adults and finds that the product moment correlation coefficient between hours of screen time per day and hours of sleep is $r=-0.47$. She tests, at the $5\%$ significance level, whether there is negative correlation in the population. For a sample of size $10$, the one-tailed $5\%$ critical value is $0.5494$.
   Software gives a $p$-value of $0.085$ for this test. Use the $p$-value to state the conclusion of the test at the $10\%$ significance level.2 marks
3. A random sample of $20$ students has product moment correlation coefficient $r=0.41$ between hours of sleep and score in a memory test. For a sample of size $20$, the critical values are: one-tailed $5\%$, $0.3783$; two-tailed $5\%$, $0.4438$.
   Test, at the $5\%$ significance level, whether there is correlation (positive or negative) between hours of sleep and memory test score.3 marks