A producer of steel cables wants to know whether the steel cables it produces have an average breaking strength of 5000 pounds. An average breaking strength of less than 5000 pounds would not be adequate, and to produce steel cables with an average breaking strength in excess of 5000 pounds would unnecessarily increase production costs. The producer collects a random sample of 64 steel cable pieces. The breaking strength for each of these cable pieces is recorded in the file P09_03.xlsx.
a. Identify the null and alternative hypotheses for this situation.
b. Using a 5% significance level, what statistical conclusion can the producer reach regarding the average breaking strength of its steel cables? Would the conclusion be any different at the 1% level? Explain your answers.