Solved Problems

A manufacturer claims their steel bars have a mean yield strength of at least 500 MPa. A sample of 25 bars has a mean strength of 495 MPa with a standard deviation of 10 MPa. Test the claim at $\alpha = 0.05$.

An engineer wants to know if there is a difference in the mean curing time of two different epoxy resins. She tests 35 samples of Resin A and finds a mean curing time of 45 hours with a standard deviation of 4 hours. She tests 40 samples of Resin B and finds a mean of 42 hours with a standard deviation of 5 hours. Test the hypothesis that the means are different at $\alpha = 0.01$.

A city regulation requires that at least 80% of new residential buildings incorporate a specific energy-efficient insulation. An inspector randomly selects 150 new buildings and finds that 110 of them have the required insulation. Is there enough evidence to conclude that the proportion is less than 80%? Test at the 0.05 level of significance.