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Answer :
The 90% confidence interval estimate for mean wake time with the drug treatment is approximately 88.0 min to 107.8 min, This suggests that the mean wake time of 101.0 min before the treatment is within the confidence interval.
To construct a 90% confidence interval estimate for the mean wake time with the drug treatment, we can use the given data.
Before treatment, the mean wake time was 101.0 min. After treatment, the sample mean wake time was 97.9 min with a standard deviation of 23.9 min.
Using the formula for confidence interval estimate:
Confidence Interval = sample mean ± (critical value) × (standard deviation / √(sample size))
First, we need to determine the critical value for a 90% confidence level. From the standard normal distribution table, the critical value for a 90% confidence level is approximately 1.645.
Calculating the confidence interval:
Sample mean = 97.9 min
Standard deviation = 23.9 min
Sample size = 19
Critical value = 1.645 (for 90% confidence level)
Confidence Interval = 97.9 ± (1.645) × (23.9 / √19)
The calculated confidence interval is approximately 88.0 min to 107.8 min.
The result suggests that the mean wake time of 101.0 min before the treatment is likely to fall within the confidence interval estimate. As the confidence interval includes the initial mean wake time, it indicates that the drug treatment does not appear to have a significant effect in reducing the mean wake time.
In summary, based on the 90% confidence interval estimate, the drug does not seem to be effective in significantly altering the mean wake time.
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