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A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects.

Before treatment, 25 subjects had a mean wake time of 104.0 minutes. After treatment, the 25 subjects had a mean wake time of 99.1 minutes with a standard deviation of 23.3 minutes.

Assume that the 25 sample values appear to be from a normally distributed population.

Construct a 90% confidence interval estimate of the mean wake time for a population with drug treatments.

- What does the result suggest about the mean wake time of 104.0 minutes before the treatment?
- Does the drug appear to be effective?

Construct the 90% confidence interval estimate of the mean wake time for a population with the treatment.

___ min < μ < ___ min

(Round to one decimal place as needed.)

Answer :

The 90% confidence interval estimate for the mean wake time for a population with the treatment is (92.8 min, 105.4 min).

To construct the 90% confidence interval for the mean wake time, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

Before treatment:

Sample size (n) = 25

Sample mean (x) = 104.0 min

After treatment:

Sample mean (x) = 99.1 min

Standard deviation (σ) = 23.3 min

Step 1: Calculate the standard error

Standard error (SE) = σ / √n

SE = 23.3 / √25 = 4.66 min

Step 2: Determine the critical value

Since we want a 90% confidence interval, the corresponding critical value can be found from the t-distribution table. For a sample size of 25 and a confidence level of 90%, the critical value is approximately 1.711.

Step 3: Calculate the confidence interval

Lower limit = x - (critical value * SE)

Lower limit = 99.1 - (1.711 * 4.66) = 92.8 min

Upper limit = x + (critical value * SE)

Upper limit = 99.1 + (1.711 * 4.66) = 105.4 min

Therefore, the 90% confidence interval estimate for the mean wake time is 92.8 min, 105.4 min.

The result suggests that the mean wake time before the treatment (104.0 min) falls within the constructed confidence interval. This means that the drug appears to be effective in reducing the mean wake time compared to before the treatment. However, further analysis and interpretation should consider factors such as sample size, clinical significance, and potential confounding variables.

Learn more about confidence intervals from the given link:

https://brainly.com/question/34299305

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