A consumer protection group randomly checks the volume of different beverages to ensure that companies are packaging the stated amount. Each individual volume is not exact, but a volume of iced tea beverages is supposed to average to 300 mL with a standard deviation of 3 mL. The consumer protection group sampled 20 beverages and found the average to be 298.4 mL. Using the given table, which of the following is the most restrictive level of significance on a hypothesis test that would indicate the company is packaging less than the required average 300 mL?Upper-Tail Valuesa5%2.5%1%Critical z-values1.651.962.58
The test statistic is z = (298.4 − 300)/(3/√20) ≈ −2.39. For a test that the mean is less than 300 mL, the 2.5% critical value is −1.96, and −2.39 is more extreme, so the test indicates underfilling at that level. The 1% critical value is −2.58, which −2.39 does not reach; therefore, 2.5% is the most restrictive listed level that still indicates less than the required average.
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