1 Maya is an athlete who competes in 1500-metre races. Last summer her practice run times had mean 4.22 minutes. Over the winter she has done some intense training to try to improve her times. A random sample of 10 of her practice run times, \(x\) minutes, this summer are summarised as follows. $$\sum x = 42.05 \quad \sum x ^ { 2 } = 176.83$$ Maya's new practice run times are normally distributed. She believes that on average her times have improved as a result of her training. Test, at the \(5 \%\) significance level, whether Maya’s belief is supported by the data.