Construct the 95% confidence interval estimate of the mean wake time for a population with the treatment.

Sinead Mcgee 2021-08-09 Answered

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<μ<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.

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Expert Answer

yagombyeR
Answered 2021-08-10 Author has 92 answers

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±tcsan. 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±tcsan
xa±tcsan=94.6±2.1824.913
94.6±15.1
=(79.5,109.7)
As, it can be observe that the confidence interval, 79.5min<μa<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.

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