Standard +0.3 This is a straightforward application of a one-sample t-test with all values provided. Students need to calculate the test statistic using the standard formula, compare to critical values from t-tables, and state a conclusion. While it's a Further Maths topic, it requires only direct substitution into a formula and table lookup with no problem-solving or conceptual challenges, making it slightly easier than average.
4 The random variable \(X\) has a normal distribution with unknown mean \(\mu\) and unknown variance \(\sigma ^ { 2 }\)
A random sample of 8 observations of \(X\) has mean \(\bar { x } = 101.5\) and gives the unbiased estimate of the variance as \(s ^ { 2 } = 4.8\)
The random sample is used to conduct a hypothesis test at the \(10 \%\) level of significance with the hypotheses
$$\begin{aligned}
& \mathrm { H } _ { 0 } : \mu = 100 \\
& \mathrm { H } _ { 1 } : \mu \neq 100
\end{aligned}$$
Carry out the hypothesis test.
4 The random variable $X$ has a normal distribution with unknown mean $\mu$ and unknown variance $\sigma ^ { 2 }$
A random sample of 8 observations of $X$ has mean $\bar { x } = 101.5$ and gives the unbiased estimate of the variance as $s ^ { 2 } = 4.8$
The random sample is used to conduct a hypothesis test at the $10 \%$ level of significance with the hypotheses
$$\begin{aligned}
& \mathrm { H } _ { 0 } : \mu = 100 \\
& \mathrm { H } _ { 1 } : \mu \neq 100
\end{aligned}$$
Carry out the hypothesis test.\\
\hfill \mbox{\textit{AQA Further Paper 3 Statistics 2023 Q4 [5]}}