Challenging +1.2 This is a standard two-sample t-test with summary statistics requiring calculation of sample means, variances, pooled variance, test statistic, and critical value comparison. While it involves multiple computational steps and understanding of hypothesis testing framework, it follows a well-established procedure taught in Further Statistics. The novel aspect of finding the range of α values adds modest difficulty beyond routine application.
A company produces packets of sweets. Two different machines, \(A\) and \(B\), are used to fill the packets. The manager decides to assess the performance of the two machines. He selects a random sample of 50 packets filled by machine \(A\) and a random sample of 60 packets filled by machine \(B\). The masses of sweets, \(x \mathrm {~kg}\), in packets filled by machine \(A\) and the masses of sweets, \(y \mathrm {~kg}\), in packets filled by machine \(B\) are summarised as follows.
$$\Sigma x = 22.4 \quad \Sigma x ^ { 2 } = 10.1 \quad \Sigma y = 28.8 \quad \Sigma y ^ { 2 } = 16.3$$
A test at the \(\alpha \%\) significance level provides evidence that the mean mass of sweets in packets filled by machine \(A\) is less than the mean mass of sweets in packets filled by machine \(B\). Find the set of possible values of \(\alpha\).
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
A company produces packets of sweets. Two different machines, $A$ and $B$, are used to fill the packets. The manager decides to assess the performance of the two machines. He selects a random sample of 50 packets filled by machine $A$ and a random sample of 60 packets filled by machine $B$. The masses of sweets, $x \mathrm {~kg}$, in packets filled by machine $A$ and the masses of sweets, $y \mathrm {~kg}$, in packets filled by machine $B$ are summarised as follows.
$$\Sigma x = 22.4 \quad \Sigma x ^ { 2 } = 10.1 \quad \Sigma y = 28.8 \quad \Sigma y ^ { 2 } = 16.3$$
A test at the $\alpha \%$ significance level provides evidence that the mean mass of sweets in packets filled by machine $A$ is less than the mean mass of sweets in packets filled by machine $B$. Find the set of possible values of $\alpha$.\\
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.\\
\hfill \mbox{\textit{CAIE FP2 2019 Q11 OR}}