Construct a 90% confidence interval of a random sample size of 19 cows with a mean of 155.526 and a standard deviation of 19.993.
Question
Construct a 90% confidence interval of a random sample size of 19 cows with a mean of 155.526 and a standard deviation of 19.993.
Solution
Sure, here are the steps to construct a 90% confidence interval:
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Identify a sample statistic: Since we are trying to estimate a population mean, we choose the sample mean (155.526) as the sample statistic.
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Select a confidence level: In this analysis, the confidence level is defined for us in the problem. We are working with a 90% confidence level.
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Find the standard deviation or standard error: Given the standard deviation of 19.993 and a sample size of 19, we can find the standard error (SE) by dividing the standard deviation by the square root of the sample size.
SE = 19.993 / sqrt(19) = 4.582
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Find the margin of error: Elsewhere on this site, we show how to compute the margin of error when the sampling distribution is approximately normal. The key steps are shown below:
Find standard deviation or standard error. Multiply it by the appropriate Z*-value (for the desired confidence level).
For a 90% confidence level, the Z*-value is 1.645.
Margin of Error (E) = Z* * SE = 1.645 * 4.582 = 7.54
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Specify the confidence interval: The range of the confidence interval is defined by the sample statistic plus the margin of error. The uncertainty is denoted by the confidence level.
Therefore, the 90% confidence interval is 155.526 ± 7.54 or (148.0, 163.1).
That means we can be 90% confident that the population mean falls between 148.0 and 163.1.
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