A random sample of 64 breaking loads, in kN, gives ∑x=5203.2\sum x=5203.2∑x=5203.2 and ∑x2=424595.16\sum x^2=424595.16∑x2=424595.16. The design value for the population mean breaking load is 82 kN. An engineer believes that the population mean may be lower.
Calculate the sample mean and sample standard deviation.
Using a Normal approximation for the sample mean and the sample standard deviation as an estimate, test the engineer's belief at the 5% significance level.