A team game involves solving puzzles to escape from a room - AQA - A-Level Maths Pure - Question 15 - 2021 - Paper 3

The sample mean (ar{x}) is calculated as:

ar{x} = \frac{6780}{100} = 67.8

The test statistic ( Z) is formulated using the formula:

$Z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}$

Substituting the values:

$Z = \frac{67.8 - 65}{\frac{11.3}{\sqrt{100}}} = \frac{2.8}{1.13} \approx 2.48$

At a 2% significance level for a two-tailed test, the critical z-values are approximately ±2.33.

The acceptance region is given by the interval [−2.33, 2.33].

Since 2.48 > 2.33, we reject the null hypothesis ( H_0).

There is sufficient evidence at the 2% level to suggest that the mean escape time has changed.