70 CHAPTER 5 Estimating Means and Proportions
- If a random sample of size n is taken from a population with a distribution
with mean μ and standard deviation σ , what is the standard deviation (or
standard error) of the sample mean equal to?
- Suppose you want to construct a confi dence interval for the mean of a
single population based on a random sample of size n from a normal
distribution. How does a 95% confi dence interval differ if the variance is
known versus when the variance is unknown?
- Describe the bootstrap principle.
- Explain how the percentile method bootstrap confi dence interval for a
parameter is obtained.
- Suppose we randomly select 25 students who are enrolled in a biostatistics
course and their heart rates are measured at rest. The sample mean is 66.9
and the sample standard deviation is S = 9.02. Assume the sample comes
from a normal distribution and the standard deviation is unknown.
Calculate a 95% two - sided confi dence interval for the mean.
- How would you compute a one - sided 95% confi dence interval of the form
( − ∞ , a] based on the data in exercise 9? Why would you use a one - sided
confi dence interval?
- The mean weight of 100 men in a particular heart study is 61 kg, with a
standard deviation of 7.9 kg. Construct a 95% confi dence interval for the
mean.
Table 5.2
Plasma Glucose Levels for Ten Diabetic
Patients
Plasma glucose (mmol/L)
Patient Before After Difference
01 4.64 5.44 0.80
02 4.95 10.01 5.06
03 5.11 8.43 3.22
04 5.21 6.65 1.44
05 5.30 10.77 5.47
06 6.24 5.69 − 0.55
07 6.50 5.88 − 0.62
08 7.15 9.98 2.83
09 6.01 8.55 2.54
10 4.90 5.10 0.20
