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2 Statistics

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Question 419

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-B​n6055​xˉ (sample mean)28.222.1​s2 (sample variance)12.89.4​​
a.

Perform a suitable test at the 5% significance level to investigate the engineer's claim. State your hypotheses, test statistic, and critical value clearly.

[6]
b.

Identify two assumptions necessary for the validity of the test performed in part (a).

[2]
Markscheme

2 Statistics Questions

  1. A Level
  2. /Maths
  3. /2 Statistics

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