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Answer :
Final answer:
A 95% confidence interval for a variable indicates where the true population mean is likely to be found with 95% confidence, but does not imply 95% of the data is within this range. The interval's width is related to the chosen confidence level and the variability of the data; more samples typically lead to narrower intervals if the error remains constant.
Explanation:
The confidence interval is a range of values, determined from sample data, that is likely to contain the population parameter with a certain level of confidence.
For example, the 95% confidence interval for 'Height' suggests that we are 95% confident the true average height of the population falls between 1.70 and 1.71 meters.
Similarly, for 'Weight', the 95% confidence interval indicates we are 95% confident the true average weight of the population lies between 75 and 77 kilograms. It is crucial to understand that the confidence interval does not mean that 95% of the data lies between these ranges, but rather that there's a 95% chance that these intervals include the true population mean.
The width of a confidence interval, such as the difference between a 90 percent confidence interval and a 95% one, depends on the confidence level and the variability of the data. A wider interval denotes greater uncertainty but higher confidence that the interval includes the true mean.
Also, when oversampling, such as increasing from 20 to 40 heads of lettuce, the confidence interval may become narrower, reflecting greater accuracy in estimating the population mean if the error bound stays the same. However, if the confidence level remains the same with more data, the confidence interval's precision improves.
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