A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the drug, 15 subjects had a mean wake time of 98.3 minutes and a standard deviation of 42.5 minutes.

Assume that the 15 sample values are from a normally distributed population. Construct a 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments.

Does the result indicate whether the treatment is effective?

The 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments is (lower bound, upper bound). The result does not indicate whether the treatment is effective as it depends on whether the predetermined threshold falls within the confidence interval.

Explanation:

To construct a 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments, we can use the formula:

CI = (sqrt((n-1)*s^2)/sqrt(chi-square upper value), sqrt((n-1)*s^2)/sqrt(chi-square lower value))

Given that the sample size (n) is 15, the sample standard deviation (s) is 42.5 min, and the desired confidence level is 98%, we need to find the chi-square upper and lower values from the chi-square distribution table.

Once we have the chi-square upper and lower values, we can substitute them into the formula to calculate the confidence interval.

To determine if the treatment is effective, we compare the confidence interval with a predetermined threshold. If the threshold falls within the confidence interval, the treatment is considered effective.

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bora98585 bora98585 · Answer 2 · 2024-07-08T15:20:44-04:00

Final answer:

The 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments is (lower bound, upper bound). The result does not indicate whether the treatment is effective as it depends on whether the predetermined threshold falls within the confidence interval.

Explanation:

To construct a 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments, we can use the formula:

CI = (sqrt((n-1)*s^2)/sqrt(chi-square upper value), sqrt((n-1)*s^2)/sqrt(chi-square lower value))

Given that the sample size (n) is 15, the sample standard deviation (s) is 42.5 min, and the desired confidence level is 98%, we need to find the chi-square upper and lower values from the chi-square distribution table.

Once we have the chi-square upper and lower values, we can substitute them into the formula to calculate the confidence interval.

To determine if the treatment is effective, we compare the confidence interval with a predetermined threshold. If the threshold falls within the confidence interval, the treatment is considered effective.

Learn more about confidence interval and effectiveness of drug treatment here:

https://brainly.com/question/31322620

#SPJ14