Hypertension A hypertensive patient has been on antihypertensive medication for several years. Her physician wants to monitor her blood pressure via weekly measurements taken at home. Each week for 6 weeks she takes several blood pressure readings and averages the readings to get a summary blood pressure for the week. The diastolic blood pressure (DBP) results are shown in Table 6.15. Table 6.15 Weekly mean DBP readings for an individual patient Week Mean DBP Mean DBP (mm Hg) Week (mm Hg) 1 89 4 84 2 88 5 82 3 81 6 89.5 Mean 85.75 sd 3.66 6.106 What is the probability that the sample mean will be within 1 unit of the population mean? 6.107 Suppose we want to choose a large enough sample so that the sample mean is within 1 unit of the population mean 99% of the time. What is the minimum sample size to achieve this goal?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Hypertension
A hypertensive patient has been on antihypertensive medication for several years. Her physician wants to monitor her
blood pressure via weekly measurements taken at home.
Each week for 6 weeks she takes several blood pressure
readings and averages the readings to get a summary blood
pressure for the week. The diastolic blood pressure (DBP)
results are shown in Table 6.15.
Table 6.15 Weekly
for an individual patient
Week Mean DBP Mean DBP
(mm Hg) Week (mm Hg)
1 89 4 84
2 88 5 82
3 81 6 89.5
Mean 85.75
sd 3.66
6.106 What is the probability that the sample mean will be
within 1 unit of the population mean?
6.107 Suppose we want to choose a large enough sample
so that the sample mean is within 1 unit of the population
mean 99% of the time. What is the minimum
achieve this goal?
Suppose the incidence rate of myocardial infarction (MI)
was 5 per 1000 among 45- to 54-year-old men in 2000.
To look at changes in incidence over time, 5000 men in this
age group were followed for 1 year starting in 2010. Fifteen
new cases of MI were found.
7.14 Of the 15 new MI cases in the preceding study,
5 died within 24 hours. Test whether the 24-hour casefatality rate changed from 2000 to 2010.
7.15 Suppose we eventually plan to accumulate 50 MI
cases during the period 2010–2015. Assume that the
24-hour case-fatality rate is truly 20% during this period.
How much power would such a study have in distinguishing
between case-fatality rates in 2000 and 2010–2015 if a
two-sided test with significance level .05 is planned?
7.16 How large a sample is needed in Problem 7.15 to
achieve 90% power?
The mean ±1 sd of ln [calcium intake (mg)] among 25
females, 12 to 14 years of age, below the poverty level is
6.56 ± 0.64. Similarly, the mean ± 1 sd of ln [calcium intake
(mg)] among 40 females, 12 to 14 years of age, above the
poverty level is 6.80 ± 0.76.
8.2 Test for a significant difference between the variances
of the two groups.
8.3 What is the appropriate procedure to test for a significant difference in means between the two groups?
8.4 Implement the procedure in Problem 8.3 using the
critical-value method.
8.5 What is the p-value corresponding to your answer to
Problem 8.4?
8.6 Compute a 95% CI for the difference in means
between the two groups.
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