Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood c
Posted: Mon Nov 15, 2021 10:53 am
Total blood volume (in ml) per body weight (in kg) is important
in medical research. For healthy adults, the red blood cell volume
mean is about 𝜇 = 28 ml/kg.† Red blood cell volume
that is too low or too high can indicate a medical problem. Suppose
that Roger has had seven blood tests, and the red blood cell
volumes were as follows.
The sample mean
is x = 33.571 ml/kg.
Let x be a random variable that represents
Roger's red blood cell volume. Assume that x has
a normal distribution and 𝜎 = 4.75. Do the data
indicate that Roger's red blood cell volume is different
from 𝜇 = 28 ml/kg? Use 𝛼 = 0.01.
(a) What is the level of significance?
State the null hypothesis H0 and the
alternate hypothesis H1
.What kind of test is this?
left-tailed test
two-tailed test
right-tailed test
(b) What sampling distribution will you use? Explain the
rationale for your choice of sampling distribution.
The Student's t, since n is
small with unknown 𝜎.
The standard normal, since we assume
that x has a normal distribution with
known 𝜎.
Compute the sample test statistic based on your choice of the
distribution. (Round your answer to two decimal places.)
(c) Find the P-value. (Round your answer to four
decimal places.)
Sketch the sampling distribution and show the area corresponding
to the P-value.
(d) Based on your answers in the previous parts, state your
decision. Will you reject or fail to reject the null hypothesis?
Are the data statistically significant at level 𝛼?
At the 𝛼 = 0.01 level, we reject the null hypothesis
and conclude the data are statistically significant.
At the 𝛼 = 0.01 level, we reject the null hypothesis
and conclude the data are not statistically
significant.
At the 𝛼 = 0.01 level, we fail to reject the
null hypothesis and conclude the data are statistically
significant.
At the 𝛼 = 0.01 level, we fail to reject the null
hypothesis and conclude the data are not statistically
significant.
(e) State your conclusion.
There is sufficient evidence at the 0.01 level to conclude that
Roger's average red cell volume differs from the average for
healthy adults.
There is insufficient evidence at the 0.01 level to conclude
that Roger's average red cell volume differs from the average for
healthy adults.
in medical research. For healthy adults, the red blood cell volume
mean is about 𝜇 = 28 ml/kg.† Red blood cell volume
that is too low or too high can indicate a medical problem. Suppose
that Roger has had seven blood tests, and the red blood cell
volumes were as follows.
The sample mean
is x = 33.571 ml/kg.
Let x be a random variable that represents
Roger's red blood cell volume. Assume that x has
a normal distribution and 𝜎 = 4.75. Do the data
indicate that Roger's red blood cell volume is different
from 𝜇 = 28 ml/kg? Use 𝛼 = 0.01.
(a) What is the level of significance?
State the null hypothesis H0 and the
alternate hypothesis H1
.What kind of test is this?
left-tailed test
two-tailed test
right-tailed test
(b) What sampling distribution will you use? Explain the
rationale for your choice of sampling distribution.
The Student's t, since n is
small with unknown 𝜎.
The standard normal, since we assume
that x has a normal distribution with
known 𝜎.
Compute the sample test statistic based on your choice of the
distribution. (Round your answer to two decimal places.)
(c) Find the P-value. (Round your answer to four
decimal places.)
Sketch the sampling distribution and show the area corresponding
to the P-value.
(d) Based on your answers in the previous parts, state your
decision. Will you reject or fail to reject the null hypothesis?
Are the data statistically significant at level 𝛼?
At the 𝛼 = 0.01 level, we reject the null hypothesis
and conclude the data are statistically significant.
At the 𝛼 = 0.01 level, we reject the null hypothesis
and conclude the data are not statistically
significant.
At the 𝛼 = 0.01 level, we fail to reject the
null hypothesis and conclude the data are statistically
significant.
At the 𝛼 = 0.01 level, we fail to reject the null
hypothesis and conclude the data are not statistically
significant.
(e) State your conclusion.
There is sufficient evidence at the 0.01 level to conclude that
Roger's average red cell volume differs from the average for
healthy adults.
There is insufficient evidence at the 0.01 level to conclude
that Roger's average red cell volume differs from the average for
healthy adults.