Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 15 subjects had a mean wake time of 102.0 min. After​ treatment, the 15 subjects had a mean wake time of 96.3 min and a standard deviation of 23.5 min. Assume that the 15 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 102.0 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.

Answer 1

Answer)

Sample mean = 96.3

Sample standard deviation = 23.5

As the population standard deviation is unknown, we will use t table to estimate the interval

Degrees of freedom is = n-1, 15-1 = 14

For df 14 and 95% confidence level

Critical value t from t table is = 2.145

Margin of error = t*(s.d/√n) = 2.145*(23.5/√15) = 13.015160534930

Confidence interval is given by

(Mean - MOE, Mean + MOE)

(83.284839465069, 109.31516053493)

Null hypothesis : Ho : u=102

Alternate hypothesis : Ha : u < 102

Since the interval contains the null hypothesised value 102

We fail to reject the null hypothesis