7. Sampling Distributions & Confidence Intervals: Mean
Confidence Intervals for Population Mean
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You want to take a trip to Paris. You randomly select 225 flights to Europe and find a mean and sample standard deviation of $1500 and $900, respectively. Construct and interpret a 95% confidence interval for the true mean price for a trip to Paris.
A
(1381.74, 1618.26)
B
(702.9, 1097.1)
C
(897.5, 902.5)
D
(1498.5, 1501.5)
Verified step by step guidance1
Identify the sample mean (\(\bar{x}\)) and sample standard deviation (s) from the problem. Here, \(\bar{x} = 1500\) and \(s = 900\).
Determine the sample size (n), which is given as 225 flights.
Since the sample size is large (n > 30), use the Z-distribution to construct the confidence interval. For a 95% confidence level, the Z-score is approximately 1.96.
Calculate the standard error of the mean (SE) using the formula: \(SE = \frac{s}{\sqrt{n}}\). Substitute the values to find SE.
Construct the confidence interval using the formula: \(\bar{x} \pm Z \times SE\). Substitute the values to find the lower and upper bounds of the confidence interval.
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