In: Statistics and Probability
A random sample was taken of 27 concrete beams produced by a certain manufacturer. Each beam in the sample was weighed (in Kg) to assess whether the concrete content was up to industry standards.Sample mean=68.4, Standard Deviation=2.6.
Construct a 95% confidence interval for the true average weight of concrete beams coming from this manufacturer. Interpret this confidence interval in the form of a sentence.The manufacturer claims that their manufacturing process is calibrated to produce average beam weights that satisfy the industry requirement of (at least) 69.5Kg per beam.Test the validity of the manufacturer’s claim using the data collected. Summarise your findings in the form of a probability statement, and write your conclusions in a way that is understandable to a quality control officer.Assess the validity of the assumptions needed to carry out the calculations.