6 Bishen believes that the mean weight of boxes of black peppercorns is 45 grams. Abi, thinking that this is not the case, weighs, in grams, a random sample of 8 boxes of black peppercorns, with the following results. $$\begin{array} { l l l l l l l l } 44 & 44 & 43 & 46 & 42 & 40 & 43 & 46 \end{array}$$

1. 1. Construct a \(95 \%\) confidence interval for the mean weight of boxes of black peppercorns, stating any assumption that you make.
   2. Comment on Bishen's belief.
2. 1. Abi claims that the mean weight of boxes of black peppercorns is less than 45 grams. Test this claim at the \(5 \%\) level of significance.
   2. If Bishen's belief is true, state, with a reason, what type of error, if any, may have occurred when conclusions to the test in part (b)(i) were drawn.
      (2 marks)