A specialized polymer resin is engineered to have a mean curing time of 142.5 minutes. A chemical engineer suspects that a recent change in the catalyst's purity has led to an increase in the mean curing time. To investigate this, a random sample of 12 batches is selected, and the curing times, t t\,t minutes, are recorded. The following summary statistics were obtained:
∑t=1758.0,∑t2=257767.0 \sum t = 1758.0, \quad \sum t^2 = 257767.0 ∑t=1758.0,∑t2=257767.0Stating your hypotheses clearly, test at the 1% level of significance whether there is evidence that the mean curing time has increased. You should assume that the curing times follow a normal distribution and that the sample variance is a valid estimate of the population variance.
