A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects.Before treatment, 18 subjects had a mean wake time of 103.0min. After treatment, the 18 subjects had a mean waketime of 93.2min and a standard deviation of 21.5min. Assume that the 18 sample values appear to be from a normallydistributed population and construct a 99% confidence interval estimate of the mean wake time for a population withdrug treatments. What does the result suggest about the mean wake time of 103.0 min before the treatment? Does thedrug appear to be effective?Construct the 99% confidence interval estimate of the mean wake time for a population with the treatment.min<�<min(Round to one decimal place as needed.) **Clinical Trial for Insomnia Treatment**A clinical trial was conducted to assess the effectiveness of a drug for treating insomnia in older individuals. Prior to treatment, the 18 subjects had a mean wake time of 103.0 minutes. After receiving the treatment, the same subjects experienced a reduced mean wake time of 93.2 minutes, with a standard deviation of 21.5 minutes.To statistically evaluate the impact of the treatment, it is important to assume that the 18 sample values are from a normally distributed population. With this assumption, we can construct a 99% confidence interval to estimate the mean wake time for a larger population receiving the drug treatment.**Objective:**Construct the 99% confidence interval estimate of the mean wake time for a population undergoing treatment.\[ \text{min} < \mu < \text{min} \](Round to one decimal place as needed.)**Analysis:**- Compare the pre-treatment mean wake time of 103.0 minutes with the post-treatment confidence interval.- Conclude whether the drug appears to be effective by determining if the pre-treatment mean falls outside the confidence interval.

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Answered: A clinical trial was conducted to test…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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

Before treatment, 18 subjects had a mean wake time of 103.0min. After treatment, the 18 subjects had a mean wake

time of 93.2min and a standard deviation of 21.5min. Assume that the 18 sample values appear to be from a normally

distributed population and construct a 99% 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 103.0 min before the treatment? Does the

drug appear to be effective?

Construct the 99% confidence interval estimate of the mean wake time for a population with the treatment.

min<�<min

(Round to one decimal place as needed.)

**Clinical Trial for Insomnia Treatment**

A clinical trial was conducted to assess the effectiveness of a drug for treating insomnia in older individuals. Prior to treatment, the 18 subjects had a mean wake time of 103.0 minutes. After receiving the treatment, the same subjects experienced a reduced mean wake time of 93.2 minutes, with a standard deviation of 21.5 minutes.

To statistically evaluate the impact of the treatment, it is important to assume that the 18 sample values are from a normally distributed population. With this assumption, we can construct a 99% confidence interval to estimate the mean wake time for a larger population receiving the drug treatment.

**Objective:**

Construct the 99% confidence interval estimate of the mean wake time for a population undergoing treatment.

\[ \text{min} < \mu < \text{min} \]

(Round to one decimal place as needed.)

**Analysis:**

- Compare the pre-treatment mean wake time of 103.0 minutes with the post-treatment confidence interval.
- Conclude whether the drug appears to be effective by determining if the pre-treatment mean falls outside the confidence interval.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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