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

Given:

• Sample mean ($\bar{x}$) = ( \frac{6780}{100} = 67.8 ) minutes
• Population mean ($\mu$) = 65 minutes
• Standard deviation ($\sigma$) = 11.3 minutes
• Sample size ($n$) = 100

Now, we use these values to formulate the test statistic.

The test statistic is calculated using the formula:
$z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} = \frac{67.8 - 65}{11.3 / \sqrt{100}} = \frac{2.8}{1.13} \approx 2.48$

For a two-tailed test at a 2% significance level, the critical values are approximately ±2.33.
Since 2.48 > 2.33, we reject $H_0$.
This indicates sufficient evidence at the 2% level to suggest that the mean escape time has changed.

There is sufficient evidence to reject the null hypothesis $H_0$ at the 2% significance level. Thus, we conclude that there is a statistically significant change in the mean time to solve the puzzles and escape from the room.