A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 13 subjects had a mean wake time of 101.0 min. After treatment, the 13 subjects had a mean wake time of 94.6 min and a standard deviation of 24.9 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 95% 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 101.0 min before the treatment? Does the drug appear to be effective? Construct the 95% confidence interval estimate of the mean wake time for a population with the treatment. min&lt;μ&lt;min (Round to one decimal place as needed.) What does the result suggest about the mean wake time of 101.0 min before the treatment? Does the drug appear to be effective? The confidence interval ▼ does not include| includes the mean wake time of 101.0 min before the treatment, so the means before and after the treatment ▼ could be the same |are different. This result suggests that the drug treatment ▼ does not have | has a significant effect.

Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 101.0 min. After​ treatment, the 13 subjects had a mean wake time of 94.6 min and a standard deviation of 24.9 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 95​% 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 101.0 min before the​ treatment? Does the drug appear to be​ effective? Construct the 95​% confidence interval estimate of the mean wake time for a population with the treatment. min&amp;lt;μ&amp;lt;min ​(Round to one decimal place as​ needed.) What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective? The confidence interval ▼ does not include| includes the mean wake time of 101.0 min before the​ treatment, so the means before and after the treatment ▼ could be the same |are different. This result suggests that the drug treatment ▼ does not have | has a significant effect.

yagombyeR · Accepted Answer

Step 1 Let μa denotes the true population mean for after treatment. Let xb― and xa― denote the sample mean for before and after treatment data. Then, provided that xb―=101.0min and xa―=94.6min. The sample size, n=13 and the sample standard deviation for after treatment data is sa=24.9min. A 95% confidence interval for the true population mean of after treatment data is given by xa―±tc⋅san. Where, tc is the critical t-score. Step 2 The critical t-score for 95% confidence level with 12 degree of freedom is tc=2.18. Now, substituting, xa―=94.6min,sa=24.9min, and n=13 in the expression, xa―±tc⋅san xa―±tc⋅san=94.6±2.18⋅24.913 ≈94.6±15.1 =(79.5,109.7) As, it can be observe that the confidence interval, 79.5min&amp;lt;μa&amp;lt;109.7min includes xb―=101.0min. Therefore, the true mean for before and after treatment could be the same. This tells that the treatment does not have the significance effect.

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

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