A student was asked to find a 98% confidence interval for widget width using data from a random sample of size n = 27. Which of the following is a correct interpretation of the interval 13.5 < μ < 22?Check all that are correct.There is a 98% chance that the mean of the population is between 13.5 and 22.With 98% confidence, the mean width of a randomly selected widget will be between 13.5 and 22.There is a 98% chance that the mean of a sample of 27 widgets will be between 13.5 and 22.With 98% confidence, the mean width of all widgets is between 13.5 and 22.The mean width of all widgets is between 13.5 and 22, 98% of the time. We know this is true because the mean of our sample is between 13.5 and 22.
Question
A student was asked to find a 98% confidence interval for widget width using data from a random sample of size n = 27. Which of the following is a correct interpretation of the interval 13.5 < μ < 22?Check all that are correct.There is a 98% chance that the mean of the population is between 13.5 and 22.With 98% confidence, the mean width of a randomly selected widget will be between 13.5 and 22.There is a 98% chance that the mean of a sample of 27 widgets will be between 13.5 and 22.With 98% confidence, the mean width of all widgets is between 13.5 and 22.The mean width of all widgets is between 13.5 and 22, 98% of the time. We know this is true because the mean of our sample is between 13.5 and 22.
Solution
The correct interpretations of the interval 13.5 < μ < 22 are:
- With 98% confidence, the mean width of all widgets is between 13.5 and 22.
This interpretation is correct because a confidence interval estimates the range in which the population parameter (in this case, the mean width of all widgets) is likely to fall, with a certain level of confidence (in this case, 98%).
- There is a 98% chance that the mean of the population is between 13.5 and 22.
This interpretation is also correct because it essentially says the same thing as the first interpretation. It states that there is a 98% probability that the true population mean falls within the given interval.
The other interpretations are incorrect because they either refer to the mean of a single randomly selected widget or the mean of a sample, neither of which is what a confidence interval estimates. A confidence interval estimates the range in which the population parameter is likely to fall, not the range in which individual observations or sample means are likely to fall.
Similar Questions
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