this situation. In the context of this situation, interpret making a Type I erro
ID: 3361988 • Letter: T
Question
this situation. In the context of this situation, interpret making a Type I error, nterplet ll The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, , is close to the target fil of 16 ounces. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hvpothesis that the mean bottle fill is the desired 16 ounces then the filler's initial setup will be readjusted T he bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test a e context of this situation, interpret making a Type I error; interpret making a Type II error 9.7 Consolidated Power, a large electric power utility, has just built a mode nlant dicch ua uter that is llowed to flow into the Atlantic Ocean. The EnvironmentalExplanation / Answer
a.
Null Hypothesis H0: The sample mean bottle fill is equal to 16 ounces.
Alternative Hypothesis Ha: The sample mean bottle fill is not equal to 16 ounces.
Degree of freedom = n - 1 = 36 - 1 = 35
Critical value of t at significance level of 0.05 and df = 35 is 2.03
We reject the null hypothesis if the test statistic is less than -2.03 or greater than +2.03.
b.
Type I error is the probability of rejecting the null hypothesis given that it is true. That is Type I error is the probability that the observed value of the test statistic will fall in the rejection region when the null hypothesis is true.
In the problem, type I error happens when the test statistic of the hypothesis test suggests to reject the null hypothesis (test statistic < - 2.08 or test statistic > 2.08) but the sample mean is near 16 ounces.
Type II error is the probability of accepting the null hypothesis given that it is false. That is, Type II error is probability that the observed value of the test statistic will not fall in the rejection region when the null hypothesis is false.
In the problem, type II error happens when the test statistic of the hypothesis test suggests to accept the null hypothesis ( - 2.08 < test statistic < 2.08) but the sample mean is not equal to 16 ounces.
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