Confidence Levels and Precision. Suppose I take a SRS of size n-144 from a popul

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Confidence Levels and Precision. Suppose I take a SRS of size n-144 from a population with a known standard deviation and I use this sample to calculate a 95% confidence interval. My 95% confidence interval for the population mean turns out to be (9.35, 10.65) 3. a. What is the value of the sample mean that this confidence interval is based on? b. what is the value of the margin of error for this 95% confidence interval? Suppose a friend of mine computes an 80% CI based on the same sample of 144 observations. which of the following is a plausible 80% CI? Be sure to explain your answer. (Note: no calculations are necessary.) C. i. (9.35, 10.43) ii. 9.25, 10.75) ii. (9.57, 10.43) iv. (9.57, 10.65) Explanation Suppose now I take a SRS of 49 observations and wish to calculate a 95% confidence interval for the true population mean. Compared to my 95% confidence interval based on a sample of size n-144, I should expect to have That is, I expect my confidence interval calculated from a sample of 49 observations to be from a sample of size n 144. d. (more/less) precision. (narrower/wider) than my confidence interval calculated

Explanation / Answer

a) sample mean = (9.35+10.65)/2 = 10

b) Margin of error = (10.65-9.35)/2 = 0.65

c) Option C, as margin of error decreases as confidence level decreases. So, width also decreases

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