Sampling and estimation — practice question

The time, measured in minutes, that a customer spends during a single visit to a particular shop is represented by the random variable $X \sim N(\mu, \sigma^2)$. In the past, the values of $\mu$ and $\sigma$ were $10.5$ and $3.8$ respectively. The shop has now moved to a new site, and the manager hopes that the revised value of $\mu$ will be above $10.5$. He chooses a random sample of $10$ customers and records how long each one stays in the shop. He then calculates the sample mean $\bar{x}$ for these $10$ times. Using a hypothesis test at the $5\%$ significance level, the manager concludes that there is enough evidence to say that the new value of $\mu$ is greater than $10.5$.