The temperature in a furnace is regulated by a control system that aims to keep the
temperature close to 800C. The temperature is measured every minute over a twohour period, during which time the minimum and maximum temperatures measured
are 782C and 819C. Analysis of the 120 measurements shows a mean value of
800.3C and a standard deviation of 7.58C. The measurements are divided into 8
data bins of 5C width with boundaries at 780.5, 785.5, 790.5, 795.5, 800.5, 805.5,
810.5, 815.5, and 820.5. The measurement count in bin 1 from 780.5C to 785.5C
was 3 and the count in the other successive bins was 8, 21, 30, 28, 19, 9, and 2.
Apply the chi-squared test to see whether the measurements fit a Gaussian distribution to (a) a 90% confidence level and (b) a 95% confidence level (think carefully
about whether the chi-squared test will be reliable for the measurement counts
observed and whether there needs to be a change in the number of data bins used for
the chi-squared test).