A factory produces metal rods with a target mean length of 12 cm. A quality control manager suspects the mean length has decreased and selects a random sample of 8 rods to test this claim. The lengths, in cm, are denoted by xxx and the following summary statistics were obtained:
∑x=94.4,∑x2=1114.2 \sum x = 94.4, \quad \sum x^2 = 1114.2 ∑x=94.4,∑x2=1114.2Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence that the mean length of the rods is less than 12 cm. You may assume that the lengths of the rods follow a normal distribution.
