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

Wribreeminsl

Wribreeminsl

Answered question

2021-08-08

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 24 subjects had a mean wake time of 104.0 min. After treatment, the 24 subjects had a mean wake time of 94.5 min and a standard deviation of 23.2 min. Assume that the 24 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 104.0 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<μ<?min

Answer & Explanation

Jaylen Fountain

Jaylen Fountain

Skilled2021-08-09Added 169 answers

Step 1
The (1α)100% confidence interval formula for the population mean when population standard deviation is not known, is defined as follows:
CI=x±tα2,n1(sn)
Here, tα2,n1 is the critical value of the t-distribution with degrees of freedom of n1 above which, 100(α2)% or α2 proportion of the observations lie, and below which, 100(1α+α2)%=100(1α2)% or (1α2) proportion of the observations lie, x is the sample mean, s is the sample standard deviation, and n is the sample size.
Step 2
According to the given question s=23.2min.
The sample mean wake time after treatment is 94.5 min.
The sample size is 24. Hence, the degrees of freedom is 23(=241).
The level of significance is 0.01.
Using the Excel formula =T.INV.2T(0.01,23) the critical value is 2.807.
Hence, the confidence interval is, x±tα2,n1(sn)=(94.5±(2.807)(23.224))
=(94.5±(2.807)(4.736))
=(94.5±13.3)
=(81.2,107.8)
Thus, the 99% confidence interval estimate of the mean wake time for a population with drug treatments is 81.2min<μ<107.8min.
Here, the value 104.0 does lies within the obtained interval.
Thus, the drug does not effectively change the wake time, by reducing it. Hence, the drug appears to be ineffective.

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