Answer :
The 84% confidence interval for the given black cherry tree heights is approximately [57.6, 98.4] feet.
A confidence interval is a range of values that we believe contains the true value of a population parameter, like the average height of black cherry trees in this case.
The confidence level, in this case, 84%, represents how confident we are that the true parameter lies within the calculated interval.
To calculate the confidence interval for the given data set, we use the formula:
[tex]\[\text{Confidence Interval} = \text{Sample Mean} \pm \text{Margin of Error}\][/tex]
where the sample mean is the average height of the trees, and the margin of error is determined by the standard error of the mean and the critical value from the t-distribution. The critical value is obtained based on the desired confidence level and degrees of freedom (which is the sample size minus one).
In this case, the calculated 84% confidence interval [57.6, 98.4] feet means that if we were to take many samples and calculate the confidence interval for each, we expect 84% of those intervals to contain the true average height of all black cherry trees.
In simpler terms, think of the confidence level like a measure of how sure we are about our estimate. A higher confidence level indicates more certainty, but it also results in a wider interval. Conversely, a lower confidence level provides a narrower interval but with less certainty.
In summary, the confidence interval helps us understand the range of values within which the true population parameter is likely to fall. The confidence level expresses our level of confidence that the parameter is within that interval. It's a way of quantifying the uncertainty associated with our estimate based on the sample data.
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The data set provided below contains the heights in feet of black cherry trees. Compute a 84% confidence interval for the given dataset
