Download Systolic Blood Pressure

Math 116 - SYSTOLIC BLOOD PRESSURE
Chapter 14 – Confidence Intervals about a Population Mean μ – sigma known
1) We want to estimate the mean systolic blood pressure of a group of overweight 18-24 year old
women. Thirty-six women from this group were selected at random and their mean systolic
blood pressure was 121 mm Hg. Assume systolic blood pressures of women of this age group
have a standard deviation of σ = 13.1 mm Hg.
a) What is the point estimate?
The point estimate is the sample mean, that is x-bar = 121
b) Verify that the requirements for constructing a confidence interval about x-bar are
satisfied.
 The sample is a simple random sample
 The value of the population standard deviation σ is known. (we’ll use z)
 The sample size is larger than 30
c) Construct a 99% confidence interval estimate for the systolic blood pressure of all
overweight women of this age group. (Are you using z or t? Why?)
The value of the population standard deviation σ is known. (We’ll use z)
x z*

n
   x z*

n
13.1
13.1
   121  2.575*
36
36
121  5.622    121  5.622
121  2.575*
115.378    126.622
For calculator feature use STAT, arrow to TESTS, and select 7:ZInterval,
select Stats enter the required information, and CALCULATE
d) The statement “99% confident” means that, if 100 samples of size __36___ were taken,
about __99___ intervals will contain the parameter μ and about __1__ will not.
e) We are __99___% confident that the mean systolic blood pressure of overweight 18-24
year old women is between ___115.38 __ and ____126.62 mm Hg__
f) With 99% confidence we can say that the mean systolic blood pressure of overweight 1824 year old women is ___121 mm Hg __ with a margin of error of __5.62_____
g) For 99% of such intervals, the sample mean would not differ from the actual population
mean by more than __5.62 mm Hg_____
h) What would be necessary in order to construct a more precise 99% confidence interval
estimate for the systolic blood pressure of this group?
If we want to keep the same degree of confidence, we have to select a larger sample
from the population. Or, if we don’t mind sacrificing our confidence, use a lower
confidence level.
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i) You know that the mean systolic blood pressure of women aged 18-24 is 114.8 mm Hg.
What does the interval constructed in part (c) suggest? Explain.
The interval (115.38, 126.62) is completely above 114.8, which suggests, with 99%
confidence, that the mean systolic blood pressure of the group of women from which the
sample was selected is higher than 114.8 mm Hg.
Chapter 15 – Sample Size
j) How large of a sample should be selected in order to be 99% confident that the point
estimate x-bar will be within 4 units of the true population mean?
 z *    2.575*13.1 
n
 
  72
4
 E  

2
2
The margin of error of the interval constructed in part (c) was 5.622. If we want our estimate to
be more precise with an error of at most 4 units we should select a sample of size 72
If we select a simple random sample of 72 women from a group of overweight 18-24 year old
women and measure their systolic blood pressures, we could say with 99% confidence that the xbar from the selected sample will be within 4 units of the true population mean systolic blood
pressure of ALL overweight 18-24 year old women
k) Circle the correct choice:
 Increasing the confidence level produces a longer/shorter
 Increasing the confidence level
increases/decreases
 Increasing the sample size
increases/decreases
interval.
the precision.
the precision.
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