CAIE
S2
2016
November
Q4
5 marks
Challenging +1.2
4 The manufacturer of a tablet computer claims that the mean battery life is 11 hours. A consumer organisation wished to test whether the mean is actually greater than 11 hours. They invited a random sample of members to report the battery life of their tablets. They then calculated the sample mean. Unfortunately a fire destroyed the records of this test except for the following partial document.
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Given that the population of battery lives is normally distributed with standard deviation 1.6 hours, find the set of possible values of the sample size, \(n\).
Edexcel
S3
2014
June
Q4
6 marks
Challenging +1.2
4. A manufacturing company produces solar panels. The output of each solar panel is normally distributed with standard deviation 6 watts. It is thought that the mean output, \(\mu\), is 160 watts.
A researcher believes that the mean output of the solar panels is greater than 160 watts. He writes down the output values of 5 randomly selected solar panels. He uses the data to carry out a hypothesis test at the \(5 \%\) level of significance.
He tests \(\mathrm { H } _ { 0 } : \mu = 160\) against \(\mathrm { H } _ { 1 } : \mu > 160\)
On reporting to his manager, the researcher can only find 4 of the output values. These are shown below
$$\begin{array} { l l l l }
168.2 & 157.4 & 173.3 & 161.1
\end{array}$$
Given that the result of the hypothesis test is that there is significant evidence to reject \(\mathrm { H } _ { 0 }\) at the \(5 \%\) level of significance, calculate the minimum possible missing output value, \(\alpha\). Give your answer correct to 1 decimal place.