Let’s consider the manufacturing setting and, specifically, the pen industry. The quality control supply chain analyst w

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Let’s consider the manufacturing setting and, specifically, the
pen industry. The quality control supply chain analyst would like
to evaluate, with a level of confidence equal to 90%, where the
average number of pens produced per hour can be found. Assume that
the pen production is normally distributed and that, based on a
sample of 24 hours, the average number of pens produced per hour is
275 with a variance of 15.
the quality control supply chain analyst would also like to make
an enquiry on a possible difference in the production numbers over
time. Assuming the pen production is normally distributed,
historical data report that around 265 pens were produced per hour.
Recently, on a sample of 48 hours, the average amount of pens is
around 266 with an associated variance of 8. The quality control
supply chain analyst would like to know if something has changed
over recent times. Please perform a hypothesis test for the
population mean with a level of significance of 0.05 while
answering the following questions