a student was asked to find a 95%confidence interval for widget width using data from a random sample of size n=23.which of the following is a correct interpretation of the interval 10.1 u 25.2?

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with 95% confidence the mean width of randomly selected widget will be seen 10.1 and 25.2

there is a 95% chance that the mean of the population is between 10.1 and 25.2

there is a 95% chance that the mean of a sample of 23 widgets will be between 10.1and 25.2

the mean width of all widgets is between 10.1and 25.2 95% of the time .we know this is true because the mean of our sample is between 10.1 25.2

The 95% confidence interval for widget width indicates a range in which the true mean width of the entire population likely falls, based on the sample of 23 widgets. There's a 95% confidence that the mean width of randomly selected widgets will be between 10.1 and 25.2, as well as a 95% chance that the true mean of the population is within this interval.

Explanation:

In the context of your question, the 95% confidence interval for the widget width of 10.1 to 25.2 suggests two main interpretations. Firstly, it means that if we were to repeat the same sampling process many times, 95% of the intervals generated from these processes would contain the true mean width of the population. Secondly, it gives us a plausible range of values for the population mean width based on the data we have from the sample size of 23.

To clarify specific points:

There is a 95% confidence that the mean width of randomly selected widget will be between 10.1 and 25.2.
There is a 95% chance that the mean of the population is between 10.1 and 25.2.
It's not accurate to say there is a 95% chance that the mean of a sample of 23 widgets will be between 10.1 and 25.2 because the confidence interval applies to the population parameter, not the sample statistic.
The statement that the mean width of all widgets is between 10.1 and 25.2, 95% of the time is not accurate as we cannot say how often the population mean falls within the interval.

Learn more about Confidence Interval here:

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