Question

Example 1: Among females in the US in a given age cohort, a diastolic blood pressure is normally distributed with mean µ = 95 mm Hg and standard deviation σ = 15 mm Hg. a) What is the probability that a randomly selected woman has a diastolic blood pressure less than 90 mm Hg? b) What is the probability that she has a diastolic blood pressure greater than 95 mm Hg? c) What is the probability that she has a diastolic blood pressure between 65 and 85 mm Hg? d) We selected a large number of random samples of size 20 from smoking females of the same cohort, and we received sampling mean equal to 92.5mm Hg. Can we not reject the hypothesis at the significance level α = 0.05 that this smoking women subgroup has the same mean as population, i.e. H0 : µ = 85.8 mm Hg against HA : µ 6= 85.8?

Example 2: Let p = 0.1 be the probability that a man in a certain age group dies in the next four years. Say we observe 30 such men and we assume independence. Consider the probability P4 that fewer than five of them die in the next four years. Which is the correct answer? A) P4 = 0.5. Explain. B) P4 > 0.5. Explain. C) P4 < 0.5. Explain.

Example 3: Among adults in the US, the distribution of albumin levels in cerebrospinal fluid is roughly symmetric with mean µ = 50mg/100ml and standard deviation σ = 12.7mg/100ml. Suppose that you select repeated samples of size 20 from this population and calculate the mean for each sample. If you were to select a large number of random samples of size 20, the sample variance of the means will be a) larger than population variance b) approximately the same as population variance c) lower than population variance

Example 4: (30 points) 2 At a hospital’s emergency room, patients are classified and 20% of them are critical, 40% are serious, and 40% are stable. Of the critical ones, 31% die; of the serious 15% die, and of stable 0.01% die. Given that a patient dies, then a) the conditional probability that a patient was classified as critical equals to 0.4 b) the conditional probability that a patient was classified as critical is less than 0.4 c) the conditional probability that a patient was classified as critical is greater than 0.4

Example 5: We have data of Serum-cholesterol (measured in mg/100ml): 124.82, 99.2, 124.2, 89.6, 94.19, 95.3, 80.6, 100.3. Which of the following statements is correct? a) the median is larger than mean b) the median is lower than mean c) the median and mean are the same

Example 6: In Denver, Colorado, the distribution of daily measures of ambient nitric acid is skewed to the right, it has mean µ = 1.81micro g/m3 and the standard deviation σ = 2.25micro g/m3 . Then the distribution of means of samples of size 30 selected from this population is a) skewed to the right more than the original sample b) skewed to the right less than the original sample

Answer #1

From a nationwide study, we know that the mean diastolic blood
pressure is 60 mm gH for children aged 5-6 years of age, and that
the measurements are normally distributed. Blood pressure
measurements were taken on 13 children aged 5-6 years living in a
specific community to determine whether their living conditions
resulted in a difference in mean blood pressure. For these children
the average diastolic blood pressure was found to be 55 mm Hg with
standard deviation 7.5 mm...

A sample of blood pressure measurements is taken from a data set
and those values (mm Hg) are listed below. The values are matched
so that subjects each have systolic and diastolic measurements.
Find the mean and median for each of the two samples and then
compare the two sets of results. Are the measures of center the
best statistics to use with these data? What else might be
better? Systolic: 138138 103103 142142 149149 129129 102102 118118
159159 155155...

1.The mean systolic blood pressure for a population of patients
(µ) from a local clinic is 130 with a standard deviation (σ) of 18.
(You will use the above information for several of the following
questions) What is the z-score for a patient with a systolic blood
pressure of 123? Rounded to the nearest hundredth.
2.71
-0.83
-0.39
-2.75
-1.14
2.
From information on a previous question: The mean systolic
blood pressure for a population of patients (µ) from a...

A researcher studying stress is interested in the blood pressure
measurements of chief executive officers (CEOs) of major
corporations. He believes that the mean systolic blood
pressure,
μ
, of CEOs of major corporations is more than
136
mm Hg, which is the value reported in a possibly outdated
journal article. He plans to perform a statistical test and
measures the systolic blood pressures of a random sample of
75
CEOs of major corporations.
Suppose that the population of systolic...

R Studio Suppose systolic blood pressure of adults has a normal
distribution with mean 130 and standard deviation 35. Research
question: Do statistics teachers have a higher average systolic
blood pressure than 130? A random sample of 100 statistics teachers
is obtained and the mean is 135. (The population standard deviation
is known, so we use Z for critical values.)
Solve the using the Confidence Interval Hypothesis Test approach
and t.test() Approach. Use the Pima.tr data set to evaluate the...

For women aged 18 to 24, systolic blood pressure (in mm Hg) is
normally distributed with a mean of 114.8 and a standard deviation
of 13.1 (based on data from the National Health Survey).
Hypertension is commonly defined as a systolic blood pressure above
140. Let X represent the systolic blood pressure of a randomly
selected woman between the ages of 18 and 24. a. Find the
probability the mean systolic blood pressure of four randomly
selected women would fall...

Many Americans have high blood pressure which can lead to a
number of serious conditions including heart attack and stroke.
There are a number of drugs available to treat high blood pressure,
but researchers are always seeking new ones with fewer side
effects. In this experiment, researchers randomly selected 20 women
from a pool with high-normal blood pressure to high blood pressure
and measured their initial systolic blood pressure (in mm of Hg).
They treated the subjects with an experimental...

When subjects were treated with a drug, their systolic blood
pressure readings (in mm Hg) were measured before and after the
drug was taken. Results are given in the table below. Assume that
the paired sample data is a simple random sample and that the
differences have a distribution that is approximately normal. Using
a
0.05
significance level, is there sufficient evidence to support the
claim that the drug is effective in lowering systolic blood
pressure?
Before
161
169
158...

Listed below are systolic blood pressure measurements (mm Hg)
taken from the right and left arms of the same woman. Assume that
the paired sample data is a simple random sample and that the
differences have a distribution that is approximately normal. Use a
0.01 significance level to test for a difference between the
measurements from the two arms. What can be concluded?
Right Arm(mm_Hg)
Left Arm(mm_Hg)
145
166
141
177
136
190
136
143
129
141
In this example,...

1. Write the corresponding letter of the distribution used to
conduct the test to answer the question or to find the probability
requested in the blank to the left of the given information. You
will only use each letter once.
a. Student’s T
b. Standard Normal
c. Chi-Square
d. Binomial
e. Poisson
_________________Suppose that a doctor claims that 17 year olds
have an average body temperature that is warmer than the commonly
accepted average human temperature of µ = 98.6...

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