[APPLET] The winning times (in hours) for a sample of 20 rando...

Question

[APPLET] The winning times (in hours) for a sample of 20 randomly selected Boston Marathon Women’s Open Division champions from 1980 to 2019 are shown in the table at the left. Assume the population standard deviation is 0.068 hour. (Source: Boston Athletic Association)

d. Does it seem likely that the population mean could be greater than 2.52 hours? Explain.

d. Does it seem likely that the population mean could be greater than 2.52 hours? Explain.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A group of researchers recorded the completion times in units of hours for 5 randomly selected hikers. Based on the sample data, the 95% confidence interval for the population mean completion time was found to be parentheses 2.642.76. Does it seem likely that the true population mean could be greater than 2.76 hours? Awesome. So it appears for this particular problem, we're ultimately trying to determine whether or not it seems likely that the true population mean could be greater than 2.76 hours. So is our answer going to be either A, yes, B, no, or C, cannot be determined? So now that we know what we're ultimately trying to solve for, which once again to note what we're trying to solve for, we are asked to interpret whether or not a population means greater than 2.76 is likely based on the given confidence interval that is provided to us by the prom itself. So with that in mind, our first step. we need to understand what a confidence interval represents. So for this particular case, a 95% confidence interval gives a range of values that is likely to contain the true population mean. Our second step is we need to analyze the value in question. So the upper bound of the interval is, which I'll call upper bound UB for short, and the upper bound is 2.76, and a value greater than 2.76 lies outside of the interval. So with that in mind, our third step is we need to draw our final conclusions. So Since, as we should note and recall, the values greater than, so once again, the values greater than 2.76 are not included in the confidence interval. And it is unlikely that the true that this true population mean is greater than 2.76 hours. And once again, since the values greater than 2.76 are not included within our confidence interval, it is unlikely that the true population mean is greater than 2.76 hours. So with that in mind, our final answer without a doubt has to be multiple choice answer letter B, which is no. And that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Population Mean

Hypothesis Testing

Standard Deviation

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