Challenging +1.2 This question requires understanding of critical regions for hypothesis tests and working backwards from a z-value to find constraints on sample size. While it involves multiple steps (identifying the test type, using the critical value z=1.645 for 5% one-tailed test, setting up inequality 1.645×1.6/√n ≤ 0.4, solving for n ≥ 43.3), these are all standard procedures for S2 level. The 'working backwards' aspect adds modest problem-solving demand beyond routine hypothesis test questions, but the mathematical techniques required are straightforward.
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.
\includegraphics[max width=\textwidth, alt={}, center]{c460afa4-1387-421d-87ac-74a64be99714-2_467_593_1612_776}
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, \(n\).
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.\\
\includegraphics[max width=\textwidth, alt={}, center]{c460afa4-1387-421d-87ac-74a64be99714-2_467_593_1612_776}
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, $n$.
\hfill \mbox{\textit{CAIE S2 2016 Q4 [5]}}