Answer to Question #109179 in Statistics and Probability for sarimon chitarree

Question

A research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has
built 16 tires and tested them to end-of-life in a road test. The sample mean and standard deviation are
60,139.7 and 3645.94 kilometers. The engineer would like to demonstrate that the mean life of this new
tire is in excess of 60,000 kilometers. Formulate and test appropriate hypotheses, and draw conclusions
using α = 0.05.

Answer 1

$H_0: \mu=a_0=60000, H_1:\mu>a_0=60000\text{ (right-tailed)}.\\ \text{We will use random variable } T=\frac{(\overline{X}-a_0)\sqrt{n}}{s}.\\ T_{obs}=\frac{(60139.7-60000)\sqrt{16}}{3645.94}\approx 0.153.\\ n-1=16-1=15\,\text{degrees of freedom}.\\ T_{cr}=T_{ct}(0.05;15)=1.7531.\\ T_{obs}<T_{cr}.\,\text{So we accept }H_0.$