Residents of the town of Alternateville have recently complained of inconsistent shipping charges at their local Post Office. They believe the scales at the Post Office are "too inconsistent", translating to unfair charges. The weight of a parcel is measured using an electronic scale that reports the true weight plus a random fluctuation (i. e., noise) which is normally distributed with a mean of zero, and independent of parcel weight. The company that manufactures the electronic scale claims that the standard deviation of the fluctuation is 2 grams and that this fluctuation "meets the industry standard". To test the manufacturer's claim, town officials measure the weight of the same package 4 times, recording the following weights (in grams):. 101.6, 97.2, 96.3, and 103.2. 7.
(a) At the α = 5% level, is there sufficient evidence to support the residents' claim?
(a) If the officials continue their investigation, estimate the result of the next weighting of the same package with 90% confidence.