It is well established that your company's current hiking shoe design lasts on average 900 miles. It is also well known that the durability of hiking shoes is normally distributed. By adding a new ingredient to the soles, you believe you can extend the life. But you want a small test of ten pairs of shoes to make it quite clear this is true before proposing extensive testing. The durability results in miles for the 10 pairs are 951, 1039, 758, 1110, 957, 1014, 1273, 1004, 853, and 1072.
a.) State the situation as a hypothesis testing problem
b.) Show in detail how to calculate the sample standard deviation.
c.) With significance level a = 0.05 would you reject the null hypothesis? Explain clearly why or why not.
d.) What is the P-value for this situation?
In details and step by step.