A sample of size =n90 is drawn from a normal population whose standard deviation is =σ9.7. The sample mean is =x38.78.Part: 0 / 20 of 2 Parts CompletePart 1 of 2(a) Construct an 80% confidence interval for μ. Round the answer to at least two decimal places.An 80% confidence interval for the mean is <<μ.
Question
A sample of size =n90 is drawn from a normal population whose standard deviation is =σ9.7. The sample mean is =x38.78.Part: 0 / 20 of 2 Parts CompletePart 1 of 2(a) Construct an 80% confidence interval for μ. Round the answer to at least two decimal places.An 80% confidence interval for the mean is <<μ.
Solution
To construct an 80% confidence interval for μ, we first need to find the standard error of the mean. The standard error (SE) is calculated as the standard deviation (σ) divided by the square root of the sample size (n).
SE = σ / √n SE = 9.7 / √90 SE = 1.023
Next, we need to find the z-score that corresponds to an 80% confidence interval. The z-score for an 80% confidence interval is 1.28 (you can find this value in a standard z-table or use a calculator that provides this value).
The confidence interval is then calculated as the sample mean (x) plus and minus the product of the z-score and the standard error.
CI = x ± (z * SE) CI = 38.78 ± (1.28 * 1.023)
Calculating the above gives us:
CI = 38.78 ± 1.31
So, the 80% confidence interval for μ is (37.47, 40.09).
Similar Questions
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