Question: To assess whether a laboratory scale is accurate we can take a standard weight know to weigh exactly 100 grams and weigh it repeatedly. Suppose that the scale readings are normally distributed with standard deviation s = 0.25 grams. If the scale is accurate then the population mean m (obtained in many repeated weightings) would be 100 grams but if the scale is inaccurate the population mean could be higher or lower.

a) The weight is weighed 25 times and the sample mean is \[\bar{X}=99.90\]. Construct a 99% confidence interval for m. Do you believe the scale is accurate based on this interval?

b) Construct a 90% confidence interval for m. Do you believe the scale is accurate based on this interval?

c) Explain why one confidence interval finds the scale accurate while the other finds the scale inaccurate.