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 inconsistent, leading 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 is independent of parcel weight. The company that manufactures the electronic scale claims that the standard deviation of the fluctuation is within 2 grams, meeting 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): 104.4, 99.8, 100.7, and 98.8.

At the specified significance level, is there sufficient evidence to support the residents' claim? Specify the null and alternative hypotheses.

To test the manufacturer's claim, we can conduct a hypothesis test comparing the sample standard deviation to the hypothesized standard deviation of 2 grams.

Explanation:

To test the manufacturer's claim about the consistency of the electronic scale, we can conduct a hypothesis test. The null hypothesis, denoted as H0, assumes that the standard deviation of the fluctuations is within 2 grams. The alternative hypothesis, denoted as Ha, assumes that the standard deviation of the fluctuations is greater than 2 grams.

To conduct the hypothesis test, we can calculate the sample standard deviation for the given weights of the packages. Then, we can compare it to the hypothesized standard deviation of 2 grams. If the sample standard deviation is significantly greater than 2 grams, we can reject the null hypothesis in favor of the alternative hypothesis.

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