Question

A clinical trial was conducted to test the nffectiveness of a drug for treating insomnia in older subjects. Before troatmentiz24 subjocts had a moan wake time of 105 o min. Atsor troatment, the 24. subiocts had a mean wake firne of 76.5 min and a standard deviation of 212 min. Assume that the 24 sample values appear to be from a normally distributed populabon and corstuct a 89% confidence inierval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake lime of tos.0 min before the troatnent? Does the drug appoar to be eflective? Construct tho 99% confidence intervai estimate of the mean wake time for a population with the treatment. min «ue min (Round to one decimal place as needed.) What does the result suggest about the moan waks time of 4050 min belore the freatment? Does the drug appeat to be ofloctive? The corfidence interval the mean wake time of 105.0 min boforo the tepatmont, so the moans before and aher the treatment dnug treatrient an efoct

Answer 1

To construct a 99% confidence interval for the mean wake time after insomnia drug treatment, calculate the standard error using the provided standard deviation and sample size, find the corresponding t-score, and apply the formula. The confidence interval does not include the original mean wake time of 105.0 minutes, suggesting the drug is effective.

Step-by-step explanation:

To construct a 99% confidence interval for the mean wake time after drug treatment for the population, you would use the formula for a confidence interval when the population standard deviation is unknown, which is based on the t-distribution because we have a small sample size. You would first calculate the standard error (SE) using the standard deviation (SD) and the square root of the sample size (n). The SE = SD / √n. Then, you find the t-score that corresponds to the 99% confidence level and 23 degrees of freedom (n-1). The confidence interval is then calculated as follows:

Confidence Interval (CI)

= mean ± (t-score * SE)
To determine the effectiveness of the drug, you would look at whether this confidence interval includes the original mean wake time before the treatment (105.0 minutes). If the confidence interval does not include 105.0 minutes, it suggests that the drug has had a significant effect in reducing wake times.

As for the requested 89% confidence interval calculation, the process would be similar, with the difference being the confidence level used to find the t-score. However, the exact results are not provided in this explanation as it would require exact calculations.