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Question
A college administrator claims that the proportion of students that are nursing
majors is greater than 40%. To test this claim, a group of 400 students are randomly
selected and its determined that 190 are nursing majors.
The following is the setup for this hypothesis test:
H0:p=0.40
Ha:p>0.40
Find the p-value for this hypothesis test for a proportion and round your answer to
3 decimal places.
The following table can be utilized which provides areas under the Standard
Normal Curve:
Correct answers:
P-value=0.001
Here are the steps needed to calculate the p-value for a hypothesis test for a
proportion:
1. Determine if the hypothesis test is left tailed, right tailed, or two tailed.
2. Compute the value of the test statistic.
3. If the hypothesis test is left tailed, the p-value will be the area under the
standard normal curve to the left of the test statistic z0
If the test is right tailed, the p-value will be the area under the standard
normal curve to the right of the test statistic z0
If the test is two tailed, the p-value will be the area to the left of −|
z0| plus the area to the right of |z0| under the standard normal curve
4. Question
5. A teacher claims that the proportion of students expected to pass an exam
is greater than 80%. To test this claim, the teacher administers the test
, to 200 random students and determines that 151 students pass the
exam.
6. The following is the setup for this hypothesis test:
7. H0:p=0.80
8. Ha:p>0.80
9. In this example, the p-value was determined to be 0.944.
10.Come to a conclusion and interpret the results for this hypothesis test for a
proportion (use a significance level of 5%)
Correct answer:
The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to support the claim.
To come to a conclusion and interpret the results for a hypothesis test for
proportion using the P-Value Approach, the first step is to compare the p-value
from the sample data with the level of significance.
The decision criteria is then as follows:
If the p-value is less than or equal to the given significance level, then the null
hypothesis should be rejected.
So, if p≤α, reject H0; otherwise fail to reject H0.
When we have made a decision about the null hypothesis, it is important to write a
thoughtful conclusion about the hypotheses in terms of the given problem's
scenario.
Assuming the claim is the null hypothesis, the conclusion is then one of the
following:
if the decision is to reject the null hypothesis, then the conclusion is that there is enough
evidence to reject the claim.
if the decision is to fail to reject the null hypothesis, then the conclusion is that there is
not enough evidence to reject the claim.
Assuming the claim is the alternative hypothesis, the conclusion is then one of the
following:
, if the decision is to reject the null hypothesis, then the conclusion is that there is enough
evidence to support the claim.
if the decision is to fail to reject the null hypothesis, then the conclusion is that there is
not enough evidence to support the claim
In this example the p-value = 0.944. We then compare the p-value to the level of
significance to come to a conclusion for the hypothesis test.
In this example, the p-value is greater than the level of significance which is 0.05.
Since the p-value is greater than the level of significance, the conclusion is to fail to
reject the null hypothesis.
Question
A police officer claims that the proportion of accidents that occur in the daytime
(versus nighttime) at a certain intersection is not 35%. To test this claim, a random
sample of 500 accidents at this intersection was examined from police records it is
determined that 156 accidents occurred in the daytime.
The following is the setup for this hypothesis test:
H0:p = 0.35
Ha:p ≠ 0.35
Find the p-value for this hypothesis test for a proportion and round your answer to
3 decimal places.
The following table can be utilized which provides areas under the Standard
Normal Curve:
Correct answers:
$\text{P-value=}0.076\ $P-value=0.076
Question
A college administrator claims that the proportion of students that are nursing
majors is greater than 40%. To test this claim, a group of 400 students are randomly
selected and its determined that 190 are nursing majors.
The following is the setup for this hypothesis test:
H0:p=0.40
Ha:p>0.40
Find the p-value for this hypothesis test for a proportion and round your answer to
3 decimal places.
The following table can be utilized which provides areas under the Standard
Normal Curve:
Correct answers:
P-value=0.001
Here are the steps needed to calculate the p-value for a hypothesis test for a
proportion:
1. Determine if the hypothesis test is left tailed, right tailed, or two tailed.
2. Compute the value of the test statistic.
3. If the hypothesis test is left tailed, the p-value will be the area under the
standard normal curve to the left of the test statistic z0
If the test is right tailed, the p-value will be the area under the standard
normal curve to the right of the test statistic z0
If the test is two tailed, the p-value will be the area to the left of −|
z0| plus the area to the right of |z0| under the standard normal curve
4. Question
5. A teacher claims that the proportion of students expected to pass an exam
is greater than 80%. To test this claim, the teacher administers the test
, to 200 random students and determines that 151 students pass the
exam.
6. The following is the setup for this hypothesis test:
7. H0:p=0.80
8. Ha:p>0.80
9. In this example, the p-value was determined to be 0.944.
10.Come to a conclusion and interpret the results for this hypothesis test for a
proportion (use a significance level of 5%)
Correct answer:
The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to support the claim.
To come to a conclusion and interpret the results for a hypothesis test for
proportion using the P-Value Approach, the first step is to compare the p-value
from the sample data with the level of significance.
The decision criteria is then as follows:
If the p-value is less than or equal to the given significance level, then the null
hypothesis should be rejected.
So, if p≤α, reject H0; otherwise fail to reject H0.
When we have made a decision about the null hypothesis, it is important to write a
thoughtful conclusion about the hypotheses in terms of the given problem's
scenario.
Assuming the claim is the null hypothesis, the conclusion is then one of the
following:
if the decision is to reject the null hypothesis, then the conclusion is that there is enough
evidence to reject the claim.
if the decision is to fail to reject the null hypothesis, then the conclusion is that there is
not enough evidence to reject the claim.
Assuming the claim is the alternative hypothesis, the conclusion is then one of the
following:
, if the decision is to reject the null hypothesis, then the conclusion is that there is enough
evidence to support the claim.
if the decision is to fail to reject the null hypothesis, then the conclusion is that there is
not enough evidence to support the claim
In this example the p-value = 0.944. We then compare the p-value to the level of
significance to come to a conclusion for the hypothesis test.
In this example, the p-value is greater than the level of significance which is 0.05.
Since the p-value is greater than the level of significance, the conclusion is to fail to
reject the null hypothesis.
Question
A police officer claims that the proportion of accidents that occur in the daytime
(versus nighttime) at a certain intersection is not 35%. To test this claim, a random
sample of 500 accidents at this intersection was examined from police records it is
determined that 156 accidents occurred in the daytime.
The following is the setup for this hypothesis test:
H0:p = 0.35
Ha:p ≠ 0.35
Find the p-value for this hypothesis test for a proportion and round your answer to
3 decimal places.
The following table can be utilized which provides areas under the Standard
Normal Curve:
Correct answers:
$\text{P-value=}0.076\ $P-value=0.076
