OCR MEI Further Statistics Major 2020 November — Question 7 10 marks

Exam BoardOCR MEI
ModuleFurther Statistics Major (Further Statistics Major)
Year2020
SessionNovember
Marks10
TopicHypothesis test of a normal distribution

7 The lengths in mm of a random sample of 6 one-year-old fish of a particular species are as follows.
\(\begin{array} { l l l l l l } 271 & 293 & 306 & 287 & 264 & 290 \end{array}\)
  1. State an assumption required in order to find a confidence interval for the mean length of one-year-old fish of this species. Fig. 7 shows a Normal probability plot for these data. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{8d36bc92-07ac-40c3-9e75-26f2bc9d2fcc-07_599_753_646_246} \captionsetup{labelformat=empty} \caption{Fig. 7}
    \end{figure}
  2. Explain why the Normal probability plot suggests that the assumption in part (a) may be valid.
  3. In this question you must show detailed reasoning. Assuming that this assumption is true, find a 95\% confidence interval for the mean length of one-year-old fish of this species.