A precision engineering firm produces titanium brackets for aerospace applications. Historical data confirms that the mass of these brackets follows a normal distribution with a mean of 840.0 g840.0 \text{ g}840.0 g and a standard deviation of 12.0 g12.0 \text{ g}12.0 g. Following a recalibration of the casting machinery, engineers suspect that the mean mass of the brackets has decreased.
A technician monitors the production line on a Monday morning and records the mass of the first 404040 brackets produced.
(i) State the sampling method used to collect this data.
(ii) Explain why this specific sample is unsuitable for conducting a formal hypothesis test to determine if the mean mass of all brackets produced has changed.
A second, independent sample of 505050 brackets is selected using a simple random sampling method. The mean mass of this sample is found to be 835.8 g835.8 \text{ g}835.8 g.
Investigate, at the 1%1\%1% level of significance, whether there is evidence that the mean mass of the brackets has decreased.
Assume that the mass of the brackets remains normally distributed and the standard deviation is unchanged at 12.0 g12.0 \text{ g}12.0 g.
