Question

refer to the accompanying data display that results from a sample of airport data speeds in mbps. the results in the screen display are based on a 95% confidence level. write a statement that correctly interprets the confidence interval
choose the correct answer below.
a. 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
b. 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
c. the limits of 13.05 mbps and 22.15 mbps contain 95% of all of the data speeds at the airports.
d. 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
(13.046,22.15)
interval
x = 17.598
sx = 16.01712719
n = 50

Explanation:

Step1: Understand confidence interval interpretation

A confidence interval is an estimate of where the population parameter (here, the population mean) lies. A 95% confidence interval means that if we were to take many samples and construct confidence intervals, about 95% of them would contain the true population parameter.

Step2: Analyze each option

• Option A: This is correct. The 95% confidence interval (13.05, 22.15) is constructed to estimate the population mean. So, 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.
• Option B: A confidence interval is about the population parameter (population mean), not the sample mean. The sample mean is a single value (in this case \(x = 17.598\)) used to construct the interval, so this option is wrong.
• Option C: The confidence level is about the method of constructing intervals (95% of intervals from repeated sampling contain the population parameter), not about the proportion of data in the population. So this option is wrong.
• Option D: Similar to option C, it misinterprets what the confidence level refers to. The confidence level is not about the proportion of data values in the population within the interval, but about the probability that the interval contains the population mean. So this option is wrong.

Answer:

A. 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.