A simple random sample produces a sample mean, xbar, of 15. A95 percent confiden

Question

A simple random sample produces a sample mean, xbar, of 15. A95 percent confidence interval for the corresponding populationmean is 15 ± 3. Which of the following statements must betrue? A. Ninety-five percent of the population measurements fallbetween 12 and 18. B. Ninety-five percent of the sample measurements fall between12 and 18. C. If 100 samples were taken, 95 of the sample means wouldfall between 12 and 18. D. P(12 <= xbar <= 18) = 0.95. E. If = 19, this xbar of 15 would be unlikely tooccur. A simple random sample produces a sample mean, xbar, of 15. A95 percent confidence interval for the corresponding populationmean is 15 ± 3. Which of the following statements must betrue? A. Ninety-five percent of the population measurements fallbetween 12 and 18. B. Ninety-five percent of the sample measurements fall between12 and 18. C. If 100 samples were taken, 95 of the sample means wouldfall between 12 and 18. D. P(12 <= xbar <= 18) = 0.95. E. If = 19, this xbar of 15 would be unlikely tooccur.

Explanation / Answer

A simple random sampleproduces a sample mean, xbar, of 15. A 95 percent confidenceinterval for the corresponding population mean is 15 ± 3.Which of the following statements must be true? A. Ninety-five percentof the population measurements fall between 12 and 18. B. Ninety-five percentof the sample measurements fall between 12 and 18. C. If 100 samples weretaken, 95 of the sample means would fall between 12 and18. D. P(12 <= xbar<= 18) = 0.95. E. If =19, this xbar of 15 would be unlikely to occur. I'm sorry I read the question wrong. The anwerwould be E because a confidence interval is always making astatement about the POPULATION mean (which would rule outanswers B, C, and D dealing with the SAMPLE mean). If the 95%confidence interval is 15 ± 3, then we are 95% confidentthat the true population mean is between the interval of 12 ad18. So, if the true population mean were 19 then obtaining asample with mean 15 would be unlikely (since it is outside of thisconfidence interval). I'm sorry I read the question wrong. The anwerwould be E because a confidence interval is always making astatement about the POPULATION mean (which would rule outanswers B, C, and D dealing with the SAMPLE mean). If the 95%confidence interval is 15 ± 3, then we are 95% confidentthat the true population mean is between the interval of 12 ad18. So, if the true population mean were 19 then obtaining asample with mean 15 would be unlikely (since it is outside of thisconfidence interval).

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