Question
In: Statistics and Probability
Patients with high blood pressure were randomly allocated to receive one of two treatments. All patients...
Patients with high blood pressure were randomly allocated to receive one of two treatments. All patients had been treated with cognitive behaviour therapy (CBT) and were then assigned (at random) to recieve no further treatment (NFT) or beta-blockers (BB). Six weeks later it was noted whether or not each of the patients showed a decrease in their blood pressure. For the NFT group 15 out of 50 patients showed a decrease after 6 weeks, whereas this happened for 26 out of 50 of the BB patients. Assume a Binomial distribution for each group, with individual sample sizes ???? and individuals parameters ???? so that the following model applies: ??1 ∼ Bi(50, ??1) ??2 ∼ Bi(50, ??2) where ??1 and ??2 denote the numbers of patient experiencing a decrease in the NFT and BB groups respectively.
1. Formulate the joint likelihood and joint log-likelihood functions.
2. Find the maximum likelihood estimates for ??1 and ??2.
3. Check that you have found maximum likelihood estimates.
4. Calculate a 95% CI for the difference in proportions (i.e. ??1 − ??2 ) of patients likely to have a decrease between the treatments.
5. What can we say about the probabilities of blood pressure decrease due to the BB treatment in question?
Solutions
orchestra answered 1 year agoRelated Solutions
Patients with high blood pressure were randomly allocated to receive one of two treatments. All patients...
Patients with high blood pressure were randomly allocated to
receive one of two treatments. All patients had been treated with
cognitive behaviour therapy (CBT) and were then assigned (at
random) to recieve no further treatment (NFT) or beta-blockers
(BB). Six weeks later it was noted whether or not each of the
patients showed a decrease in their blood pressure. For the NFT
group 15 out of 50 patients showed a decrease after 6 weeks,
whereas this happened for 26 out...
Of 116 randomly selected adults, 34 were found to have high blood pressure. Find a 98%...
Of 116 randomly selected adults, 34
were found to have high blood pressure. Find a 98% confidence
interval for the percentage of adults that have high blood
pressure.
A. 19.5% to
39.1%
B. 21.0% to 37.6%
C. 22.3% to
36.2%
D. 25.3% t0 33.3%
Drugs are often used for reducing the blood pressure of hypertensive patients (those with high blood...
Drugs are often used for reducing the blood pressure of
hypertensive patients (those with high blood pressure). An
experiment was run to investigate the effect of Drug (A or B) and
Dose Level (Low or High) on the reduction in blood pressure. The
experiment was conducted separately for the 36 patients who had
mild hypertension and the 24 patients who had severe hypertension
as the researcher suspected that results may differ for the two
groups. For this design, there are:
In one population, it is found that 6% of all people have high blood pressure and...
In one population, it is found that 6% of all people have high
blood pressure and 40% are overweight. Four percent suffer from
both con- ditions. What is the probability that a randomly selected
person from this population will have high blood pressure given
that he is not over- weight?
Please explain :)
Of all people in one population, 21% have high blood pressure and 36% are overweight. In...
Of all people in one population, 21% have high blood pressure
and 36% are overweight. In addition, 42% of people who are
overweight also have high blood pressure. Let H represent the event
that a person has high blood pressure, and O represent the event
that a person is overweight. In each part of this question, you
must first express each probability in terms of the events H and O
and justify any computation through the use of a formula....
A double blind, randomly allocated medical experiment is comparing two possible treatments for an immune-system disorder....
A double blind, randomly allocated medical experiment is
comparing two possible treatments for an immune-system disorder.
Patients are randomly assigned treatments.
Response
No Response
Treatment A
45
120
Treatment B
95
70
Show that Treatment B has the better response rate.
One with a systolic blood pressure greater than 129 is considered to have high blood pressure....
One with a systolic blood pressure greater than 129 is
considered to have high blood pressure. A study recorded
the systolic blood pressures of 14 randomly selected Americans,
which yielded a mean of 131.57 with standard deviation 15.88.
Conduct a hypothesis test to see if you can say
that Americans, on average, have high blood pressure.
1.Write the hypotheses for this test.
2.What is the test statistic?
3.What is the p-value?
4.Using α = 0.05, decide whether or not to...
You test a new drug to reduce blood pressure. A group of 15 patients with high...
You test a new drug to reduce blood pressure. A group of 15
patients with high blood pressure report the following systolic
pressures (measured in mm Hg): before medication: after medication:
change: ̄y s 187 120 151 143 160 168 181 197 133 128 130 195 130
147 193 187 118 147 145 158 166 177 196 134 124 133 196 130 146 189
156.40 0 2 4 -2 2 2 4 1 -1 4 -3 -1 0 1 4...
3. Three different treatments for hypertension (high blood pressure) are being tested. A medical researcher takes...
3. Three different treatments for hypertension (high blood
pressure) are being tested. A medical researcher takes volunteers
and randomly assigns them into groups taking treatment A, B, and C.
The reduction in blood pressure is measured for each patient with
the following results:
> d patient treatment reduction 1 1 A 7.0 2 2 A 7.9 3 3 A 5.0
4 4 A 8.3 5 5 A 3.3 6 6 A 2.8 4 7 7 A 3.9 8 8 A...
the probability that man has high blood pressure is 0.25 and If we randomly select 7...
the
probability that man has high blood pressure is 0.25 and If we
randomly select 7 men. Find the probability that 2 men with high
blood pressure. Also, find the expected number of men with high
blood pressure.
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