A sustainable energy engineer claims that high-efficiency PV-A solar panels generate an average of more than 4.5 kWh per day more than standard PV-B panels.
A study of the performance of 60 PV-A panels and 55 PV-B panels is conducted over a peak season. The daily energy output, y y\,y for PV-A and z z\,z for PV-B, is recorded in kWh. The findings are summarized in the table below.
Panel Typenxˉ (sample mean)s2 (sample variance)PV-A6028.212.8PV-B5522.19.4 \begin{array}{|c|c|c|c|} \hline \text{Panel Type} & n & \bar{x} \text{ (sample mean)} & s^2 \text{ (sample variance)} \\ \hline \text{PV-A} & 60 & 28.2 & 12.8 \\ \hline \text{PV-B} & 55 & 22.1 & 9.4 \\ \hline \end{array} Panel TypePV-APV-Bn6055xˉ (sample mean)28.222.1s2 (sample variance)12.89.4Perform a suitable test at the 5% significance level to investigate the engineer's claim. State your hypotheses, test statistic, and critical value clearly.
Identify two assumptions necessary for the validity of the test performed in part (a).
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.