5 The amount of money, in dollars, spent by a customer on one visit to a certain shop is modelled by the distribution \(\mathrm { N } ( \mu , 1.94 )\). In the past, the value of \(\mu\) has been found to be 20.00 , but following a rearrangement in the shop, the manager suspects that the value of \(\mu\) has changed. He takes a random sample of 6 customers and notes how much they each spend, in dollars. The results are as follows.
15.50
17.60
17.30
22.00
23.50
31.00 The manager carries out a hypothesis test using a significance level of \(\alpha \%\). The test does not support his suspicion. Find the largest possible value of \(\alpha\).