Hypothesis test for correlationEdexcel A-Level Maths: Mind map

Exam questions on Hypothesis test for correlation

1. A student records, on 20 randomly chosen days, the daily maximum temperature and the number of ice creams sold at a kiosk. The product moment correlation coefficient is $r=0.52$. The student tests for correlation at the 5% significance level. For a two-tailed test with sample size 20, the critical value at the 5% level is $0.4438$.
   Carry out the test and state your conclusion in context.2 marks
2. A teacher records, for 12 students, the time spent on screens each night and the score in a memory test. The product moment correlation coefficient is $r=-0.62$. The teacher believes that more screen time is associated with lower scores, and tests this at the 5% significance level. For a one-tailed test with sample size 12, the critical value at the 5% level is $0.4973$.
   A student says: 'The result proves that spending more time on screens makes scores worse.' Comment on this statement.2 marks
3. A farmer records the amount of fertiliser, $x$ kg per hectare, and the yield, $y$ tonnes per hectare, on 8 fields. The data are $(20,4.1)$, $(30,4.9)$, $(40,4.4)$, $(50,5.8)$, $(60,5.1)$, $(70,5.6)$, $(80,5.9)$, $(90,5.3)$. For a one-tailed test with sample size 8, the critical value is $0.6215$ at the 5% level and $0.7887$ at the 1% level.
   Use your calculator to find the product moment correlation coefficient $r$, and state suitable hypotheses for a test of whether more fertiliser is associated with a greater yield.3 marks