Moderate -0.3 This is a standard one-sample t-test with clearly stated hypotheses (H₀: μ = 79 vs H₁: μ > 79). Students must calculate sample mean and standard deviation, apply the t-test formula, compare to critical value, and state the normality assumption. While it requires multiple steps, it's a textbook application of a core S2 technique with no conceptual surprises, making it slightly easier than average.
Judith, the village postmistress, believes that, since moving the post office counter into the local pharmacy, the mean daily number of customers that she serves has increased from \(79\).
In order to investigate her belief, she counts the number of customers that she serves on \(12\) randomly selected days, with the following results.
\(88 \quad 81 \quad 84 \quad 89 \quad 90 \quad 77 \quad 72 \quad 80 \quad 82 \quad 81 \quad 75 \quad 85\)
Stating a necessary distributional assumption, test Judith's belief at the \(5\%\) level of significance. [9 marks]
Judith, the village postmistress, believes that, since moving the post office counter into the local pharmacy, the mean daily number of customers that she serves has increased from $79$.
In order to investigate her belief, she counts the number of customers that she serves on $12$ randomly selected days, with the following results.
$88 \quad 81 \quad 84 \quad 89 \quad 90 \quad 77 \quad 72 \quad 80 \quad 82 \quad 81 \quad 75 \quad 85$
Stating a necessary distributional assumption, test Judith's belief at the $5\%$ level of significance. [9 marks]
\hfill \mbox{\textit{AQA S2 2010 Q1 [9]}}