Reference no: EM131042403

James and his sister, Alice, each deliver 30 papers on their evening paper rounds and each are paid the same amount. one evening, Alison claims this system of equal payment to be unfair as her round takes on average longer than that of her brother james. To test her claim their father , unknown to them, records their delivery times for 12 consecutive days. One of Alison's times had to be discounted as the front tire of her bicycle was punctured. The recorded times, in minutes, were shown below

Delivery times ( minutes)

James 45 30 39 32 34 43 38 35 43 39 32 34
Alice 49 42 39 45 38 49 43 36 33 41 36

Assuming each child's delivery times are normally distributed with the same known standard deviation of 5 minutes, test whether Alison's claim is justified, using a 5% level of significance.