A certain genetic characteristic of a particular plant can appear in one of three forms (phenotypes). A researcher has d
Posted: Wed May 11, 2022 1:33 pm
A certain genetic characteristic of a particular plant can
appear in one of three forms (phenotypes). A researcher has
developed a theory, according to which the hypothesized proportions
are
p1 = 0.25,
p2 = 0.50,
and
p3 = 0.25.
A random sample of 200 plants yields
𝜒2 = 5.37.
(a)
Carry out a test of the null hypothesis that the theory is
correct, using level of significance
𝛼 = 0.05.
Use technology to calculate the P-value. (Round
your answer to four decimal places.)
P-value =
What can you conclude?
Fail to reject H0. We have convincing
evidence that the theory is
incorrect.Reject H0. We do not have
convincing evidence evidence that the theory is
incorrect. Fail to
reject H0. We do not have convincing
evidence that the theory is
incorrect.Reject H0. We have convincing
evidence that the theory is incorrect.
(b)
Suppose that a random sample of 300 plants had resulted in the
same value of
𝜒2.
How would the analysis and conclusion differ from those in
part (a)?
The analysis and conclusions would not change.The previous
analysis did not yield a significant result and the null hypothesis
failed to be rejected. The new analysis would yield a significant
result and the null hypothesis would be
rejected. The previous analysis
yielded a significant result and the null hypothesis failed to be
rejected. The new analysis would not yield a significant result and
the null hypothesis would be rejected.The previous analysis did not
yield a significant result and the null hypothesis was rejected.
The new analysis would yield a significant result and the null
hypothesis would fail to be rejected.The previous analysis yielded
a significant result and the null hypothesis was rejected. The new
analysis would not yield a significant result and the null
hypothesis would fail to be rejected.
appear in one of three forms (phenotypes). A researcher has
developed a theory, according to which the hypothesized proportions
are
p1 = 0.25,
p2 = 0.50,
and
p3 = 0.25.
A random sample of 200 plants yields
𝜒2 = 5.37.
(a)
Carry out a test of the null hypothesis that the theory is
correct, using level of significance
𝛼 = 0.05.
Use technology to calculate the P-value. (Round
your answer to four decimal places.)
P-value =
What can you conclude?
Fail to reject H0. We have convincing
evidence that the theory is
incorrect.Reject H0. We do not have
convincing evidence evidence that the theory is
incorrect. Fail to
reject H0. We do not have convincing
evidence that the theory is
incorrect.Reject H0. We have convincing
evidence that the theory is incorrect.
(b)
Suppose that a random sample of 300 plants had resulted in the
same value of
𝜒2.
How would the analysis and conclusion differ from those in
part (a)?
The analysis and conclusions would not change.The previous
analysis did not yield a significant result and the null hypothesis
failed to be rejected. The new analysis would yield a significant
result and the null hypothesis would be
rejected. The previous analysis
yielded a significant result and the null hypothesis failed to be
rejected. The new analysis would not yield a significant result and
the null hypothesis would be rejected.The previous analysis did not
yield a significant result and the null hypothesis was rejected.
The new analysis would yield a significant result and the null
hypothesis would fail to be rejected.The previous analysis yielded
a significant result and the null hypothesis was rejected. The new
analysis would not yield a significant result and the null
hypothesis would fail to be rejected.