Question

An herbal medicine is tested on 10 patients with sleeping disorders. The table below shows the hours of sleep patients got during one night without using the

herbal medicine and the hours of sleep the same patients got on another night after the herbal medicine was administered. Assume underlying normal distributions. Remember the applets will only accept one word labels. Data must be organized in columns.

Patient 1 2 3 4 5 6 7 8 9 10

Hours

without 1.0 1.4 3.4 3.7 5.1 5.1 5.2 5.3 5.5 5.8

Hours

with 2.9 3.3 3.5 4.4 5.0 5.0 5.2 5.3 6.0 6.5

a. At a= 0.01, does the herbal medicine increase the number of hours of sleep during one night?

b. Construct a 95% confidence interval for the mean difference.

c. What is the point estimate for this interval?

d. What is the margin of error for this interval?

e. Interpret the confidence interval in the context of this problem.

Answer 1

a ) let us consider d = sleep hours without - sleep hours with

the null and alternative hypothesis is

Ho:ud= 0

Ha:ud<0

using excel>Addin>phstat>two sample test

we have

Paired t Test
Data
Hypothesized Mean Difference	0
Level of significance	0.05
Intermediate Calculations
Sample Size	10
DBar	-0.5600
Degrees of Freedom	9
SD	0.7706
Standard Error	0.2437
t Test Statistic	-2.2981
Lower-Tail Test
Lower Critical Value	-1.8331
p-Value	0.0236
Reject the null hypothesis

since p value of test stat is 0.0236 >0.01 so we do not have sufficient evidence to say that the herbal medicine increase the number of hours of sleep during one night

b ) t at 95% with 9 df is 2.262

95% confidence interval = -0.56 +/- 2.262*0.2437 = (-1.111,-0.009)

c. the point estimate for this interval is -0.56

d. the margin of error for this interval is 2.262*0.2437 = 0.551

e. we are 95% confident that the difference in sleep hours for with or without medicine lies in between (-1.111,-0.009)