Standard +0.8 This is a two-sample t-test requiring calculation of summary statistics from raw data, correct identification of hypotheses, appropriate test selection, and statement of assumptions. While methodical, it requires multiple computational steps, proper interpretation of 'greater than' for a one-tailed test, and understanding of when two-sample tests apply (not paired despite the title). The 10-mark allocation and need to state validity assumptions elevate this above routine exercises.
6 A scientist is investigating the masses of a particular type of fish found in lakes \(A\) and \(B\). He chooses a random sample of 10 fish of this type from lake \(A\) and records their masses, \(x \mathrm {~kg}\), as follows.
0.9
1.8
1.8
1.9
2.1
2.4
2.6
2.2
2.5
3.0
The scientist also chooses a random sample of 12 fish of this type from lake \(B\), but he only has a summary of their masses, \(y \mathrm {~kg}\), as follows.
$$\sum y = 24.48 \quad \sum y ^ { 2 } = 53.75$$
Test at the \(10 \%\) significance level whether the mean mass of fish of this type in lake \(A\) is greater than the mean mass of fish of this type in lake \(B\). You should state any assumptions that you need to make for the test to be valid. [0pt]
[10]
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
6 A scientist is investigating the masses of a particular type of fish found in lakes $A$ and $B$. He chooses a random sample of 10 fish of this type from lake $A$ and records their masses, $x \mathrm {~kg}$, as follows.\\
0.9\\
1.8\\
1.8\\
1.9\\
2.1\\
2.4\\
2.6\\
2.2\\
2.5\\
3.0
The scientist also chooses a random sample of 12 fish of this type from lake $B$, but he only has a summary of their masses, $y \mathrm {~kg}$, as follows.
$$\sum y = 24.48 \quad \sum y ^ { 2 } = 53.75$$
Test at the $10 \%$ significance level whether the mean mass of fish of this type in lake $A$ is greater than the mean mass of fish of this type in lake $B$. You should state any assumptions that you need to make for the test to be valid.\\[0pt]
[10]\\
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 Further Paper 4 2021 Q6 [10]}}