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Answer :
Final answer:
We have constructed a 90% confidence interval for the mean wake time after the treatment. The interval is (87.78 min, 107.82 min), measured in minutes. This interval gives an estimate of the range in which the true population mean is likely to fall.
Explanation:
The subject of the question is related to statistics in probability theory, specifically to the concept of confidence intervals. The question asks for a 90% confidence interval estimate of the mean wake time after treatment.
To construct the confidence interval, we first need to calculate the standard error (SE) of the mean, using the formula SE = SD / sqrt(n), where SD is the standard deviation and n is the sample size. In this case, SE = 20.5 / sqrt(14) = 5.49 (approximately). Then, we find the z-score associated with a 90% confidence interval, which is ±1.645.
Thus, the confidence interval for the mean is defined by the formula: Confidence Interval = M ± (Z * SE), where M is the mean, Z is the z-score, and SE is the standard error. So, we can now calculate the Confidence Interval = 97.8 ± (1.645 * 5.49). This gives us the confidence interval of (87.78 min, 107.82 min).
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