WJEC Further Unit 5 2024 June — Question 1 9 marks

Exam BoardWJEC
ModuleFurther Unit 5 (Further Unit 5)
Year2024
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConfidence intervals
TypeCalculate CI from summary stats
DifficultyModerate -0.3 This is a straightforward confidence interval question with known variance, requiring standard formula application and basic interpretation. Part (a) is routine calculation (z-interval with given σ²), part (b) tests textbook knowledge (use t-distribution, use sample variance), and part (c) requires simple contextual reasoning about statistical vs practical significance. While it's a multi-part question worth 9 marks total, each component is standard A-level statistics with no novel problem-solving required, making it slightly easier than average.
Spec5.05d Confidence intervals: using normal distribution

During practice sessions, a basketball coach makes his players run several 'line drills'.
  1. He records the times taken, in seconds, by one of his players to run the first 'line drill' on a random sample of 8 practice sessions. The results are shown below. 29.4 \quad 31.1 \quad 28.9 \quad 30.0 \quad 29.9 \quad 30.4 \quad 29.7 \quad 30.2 Assuming that these data come from a normal distribution with mean \(\mu\) and variance 0.6, calculate a 95\% confidence interval for \(\mu\). [5]
  2. State the two ways in which the method used to calculate the confidence interval in part (a) would change if the variance were unknown. [2]
  3. During a practice session, a player recorded a mean time of 35.6 seconds for 'line drills'.
    1. Give a reason why this player may not be the same as the player in part (a).
    2. Give a reason why this player could be the same as the player in part (a). [2]

Question 1:
AnswerMarks
19
Question 1:
1 | 9
During practice sessions, a basketball coach makes his players run several 'line drills'.

\begin{enumerate}[label=(\alph*)]
\item He records the times taken, in seconds, by one of his players to run the first 'line drill' on a random sample of 8 practice sessions. The results are shown below.

29.4 \quad 31.1 \quad 28.9 \quad 30.0 \quad 29.9 \quad 30.4 \quad 29.7 \quad 30.2

Assuming that these data come from a normal distribution with mean $\mu$ and variance 0.6, calculate a 95\% confidence interval for $\mu$. [5]

\item State the two ways in which the method used to calculate the confidence interval in part (a) would change if the variance were unknown. [2]

\item During a practice session, a player recorded a mean time of 35.6 seconds for 'line drills'.
\begin{enumerate}[label=(\roman*)]
\item Give a reason why this player may not be the same as the player in part (a).
\item Give a reason why this player could be the same as the player in part (a). [2]
\end{enumerate}
\end{enumerate}

\hfill \mbox{\textit{WJEC Further Unit 5 2024 Q1 [9]}}