7. \section*{In this question you must show detailed reasoning.} On the manufacturer's website, it is claimed that the average daily electricity consumption of a particular model of fridge is 1.25 kWh (kilowatt hours). A researcher at a consumer organisation decides to check this figure. A random sample of 40 fridges is selected. Summary statistics for the electricity consumption \(x \mathrm { kWh }\) of these fridges, measured over a period of 24 hours, are as follows.
\(\Sigma x = 51.92 \quad \Sigma x ^ { 2 } = 70.57\) Carry out a test at the \(5 \%\) significance level to investigate the validity of the claim on the website.
[0pt] [10]