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).
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.