Question

It is claimed that a new treatment is more effective
than the standard treatment for prolonging the

lives of terminal cancer patients. The standard treatment has been
in use for a long time, and from

records in medical journals, the mean survival period is known to
be 4.2 years. The new treatment

is administered to 80 patients and their duration of survival
recorded. The sample mean and the

standard deviation are found to be 4.5 and 1.1 years, respectively.
Answer the following questions.

(a) Define µ in the context of the problem and formulate the null
and alternative hypotheses.

(b) State the Type I and Type II errors for this problem and tell
why Type I error is more serious.

(c) State the Z-test statistic for this problem and tell its
distribution.

(d) Is the small, large or both small and large value of the Z-test
statistic that will lead us to reject

the null hypothesis?

(e) Suppose the significance level is 0.05. Determine the critical
value for the rejection region and

write down the decision rule.

(f) Calculate the value of Z-test statistic from the available
data.

(g) Determine whether or not the null hypothesis is rejected at the
significance level and tell why.

(h) Calculate the P-value and do the hypothesis testing based on
the P-value.

(i) Express the conclusion in the context of the problem, using
common English.

Answer #1

It is claimed that a new treatment for prolonging the lives of
cancer patients is more effective than the standard one. Records of
earlier
research show the mean survival period to have been 4.3 years with
the standard treatment. The new teatment is administered to a
sample
of 20 patients, and the durations of their survival are recorded.
The sample mean is 4.6 years, and the standard deviation is 1.2
years.
Is the claimed effectiveness of the new method supported...

steel factory produces iron rods that are supposed to
be 36 inches long. The machine that makes
these rods does not produce each rod exactly 36 inches long. The
lengths of these rods vary slightly.
It is known that when the machine is working properly, the mean
length of the rods is 36 inches.
According to design, the standard deviation of the lengths of all
rods produced on this machine is
always equal to .05 inches. The quality control department...

A hospital reported that the normal death rate for patients with
extensive burns (more than 40% of skin area) has been significantly
reduced by the use of new fluid plasma compresses. Before the new
treatment, the mortality rate for extensive burn patients was about
60%. Using the new compresses, the hospital found that only 44 of
95 patients with extensive burns died. Use a 1% level of
significance to test the claim that the mortality rate has dropped
since using...

A hospital reported that the normal death rate for patients with
extensive burns (more than 40% of skin area) has been significantly
reduced by the use of new fluid plasma compresses. Before the new
treatment, the mortality rate for extensive burn patients was about
60%. Using the new compresses, the hospital found that only 44 of
95 patients with extensive burns died. Use a 1% level of
significance to test the claim that the mortality rate has dropped
since using...

A hospital reported that the normal death rate for patients with
extensive burns (more than 40% of skin area) has been significantly
reduced by the use of new fluid plasma compresses. Before the new
treatment, the mortality rate for extensive burn patients was about
60%. Using the new compresses, the hospital found that only 44 of
93 patients with extensive burns died. Use a 1% level of
significance to test the claim that the mortality rate has dropped
since using...

The mean survival time for patients with a particular form of
disease is 4 years. A new treatment is tried on 20 patients with
this particular disease and their average survival time is 4.7
years with a standard deviation of 1.5 years.
(a) State the direction of the alternative hypothesis to test if
the new treatment constitutes a significant improvement in survival
time. Type gt (greater than), ge (greater than or equal to), lt
(less than), le (less than or...

10) (1 point) A psychologist has developed a new treatment for
acrophobia (the extreme fear of heights) and wants to compare the
results of this new treatment to the results of the standard
treatment. A study is conducted where a random sample of 12
patients undergo the new treatment and their improvement scores on
a diagnostic test are compared to a control sample of 13 patients
who received the standard treatment. Summary scores for both groups
are shown in the...

A hospital reported that the normal death rate for patients with
extensive burns (more than 40% of skin area) has been significantly
reduced by the use of new fluid plasma compresses. Before the new
treatment, the mortality rate for extensive burn patients was about
60%. Using the new compresses, the hospital found that only 42 of
89 patients with extensive burns died. Use a 1% level of
significance to test the claim that the mortality rate has
dropped.
What are...

A researcher is creating a new treatment protocol for
Myelodysplastic Syndrome (MDS), a form of preleukemia.
Following the old treatment protocol, 32% of patients with MDS will
develop leukemia within 5 years of MDS diagnosis. He believes his
new treatment protocol will lead to fewer MDS patients developing
leukemia. He takes a random sample of 100 individuals on his new
treatment protocol. Of these 100 individuals, 27 develop leukemia
within 5 years of MDS diagnosis.
Create a 99% confidence interval...

To find out if a new serum will stop leukemia, nine patients are
selected who are in an advanced stage of the disease. Five patients
receive the treatment and four do not. Survival times, in years,
from the moment the experiment begins are
WITH TREATMENT 2.1 | 5.3 | 1.4 | 4.6 | 0.9
WITHOUT TREATMENT 1.9 | 0.5 | 2.8 | 3.1 |
Use the Wilcoxon rank-sum test statistic at a
significance level of 0.05 to determine if the...

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