Jim and his sister, Alison, 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. Jim's average delivery time was 38 minutes whereas Alison's average delivery time was 40 minutes. The respective standard deviations were 5 minutes and 4 minutes.
a) At a 5% level of significance test whether Alison's claim is justified.
b) If Alison claims that the average times are different (rather than specifically saying that one is greater than the other), how would your result from (a) change? Explain in details.