Aerospace engineers are investigating the relationship between the wing-tip vibration frequency (vvv, in Hz) and the internal cabin noise level (NNN, in dB) of a prototype long-range drone. In a series of 50 flight trials, the product moment correlation coefficient was calculated to be r=0.354r = 0.354r=0.354. Assuming the data is drawn from a population follows a bivariate normal distribution, perform a hypothesis test at the 1% level of significance to determine whether there is evidence of a positive correlation between vibration frequency and cabin noise. The critical value for the product moment correlation coefficient at the 1% significance level for a sample size of 50 is 0.3281.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.