Refer to the accompanying data display that results from a sample of airport data speeds in TInterval Mbps. The results in the screen display are based on a \( 95 \% \) confidence level. Write a statement that correctly interprets the confidence interval. \[ \begin{array}{l} \frac{(13.046,22.15)}{x}=17.598 \\ S x=16.01712719 \\ n=50 \end{array} \] Choose the correct answer below. A. We have \( 95 \% \) confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the sample mean of the data speeds at the airports. B. The limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports. C. We have \( 95 \% \) confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports. D. The limits of 13.05 Mbps and 22.15 Mbps contain \( 95 \% \) of all of the data speeds at the airports.
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We have \( 95 \% \) confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports. This means that if we were to take many samples and construct confidence intervals in the same way, approximately \( 95 \% \) of those intervals would encompass the actual average data speed across all airports. Confidence intervals are a fantastic tool for understanding uncertainty in statistics! Remember, the key is that it doesn’t mean that \( 95 \% \) of the individual data speeds fall within that range (which is a common misconception). Rather, it’s all about providing a plausible range for the population mean based on our sample.
