Question

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

2121

subjects had a mean wake time of

102.0102.0

min. After​ treatment, the

2121

subjects had a mean wake time of

95.695.6

min and a standard deviation of

20.120.1

min. Assume that the

2121

sample values appear to be from a normally distributed population and construct a

9595​%

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

102.0102.0

min before the​ treatment? Does the drug appear to be​ effective?Construct the

9595​%

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

nothing

minless than<muμless than<nothing

min

​(Round to one decimal place as​ needed.)

What does the result suggest about the mean wake time of

102.0102.0

min before the​ treatment? Does the drug appear to be​ effective?The confidence interval

▼

does not include

includes

the mean wake time of

102.0102.0

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

▼

Enter your answer in each of the answer boxes

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 95.6

sample standard deviation = s = 20.1

sample size = n = 21

Degrees of freedom = df = n - 1 = 21 - 1 = 20

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t_0.025,20 = 2.086

Margin of error = E = t_/2,df * (s /n)

= 2.086 * ( 20.1/ 21)

Margin of error = E = 9.1

The 95% confidence interval estimate of the population mean is,

- E < < + E

95.6 - 9.1 < < 95.6 + 9.1

( 86.5 min. < < 104.7 min. )

The confidence interval include the mean wake time of 102.0 min.before the treatment so the means before and after the treatment are same this result suggests that the drug treatment does not have a significant effect