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).
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.