MATH 225N; Week 7 Assignment -
Conduct a Hypothesis Test for
Proportion- P-Value Approach
(Q&A) Latest 2022/2023
, Week 7 Assignment -Conduct a Hypothesis Test for Proportion- P-Value Approach
Determine the p-value for a hypothesis test for proportion
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
For this example, the test is a right tailed test and the test statistic, rounding to two
decimal places,
is z=0.475−0.400.40(1−0.40)400‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ ≈3.06. Thus
the p-value is the area under the Standard Normal curve to the right of a z-score of
3.06.
From a lookup table of the area under the Standard Normal curve, the
corresponding area is then 1 - 0.999 = 0.001.
Conduct a Hypothesis Test for
Proportion- P-Value Approach
(Q&A) Latest 2022/2023
, Week 7 Assignment -Conduct a Hypothesis Test for Proportion- P-Value Approach
Determine the p-value for a hypothesis test for proportion
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
For this example, the test is a right tailed test and the test statistic, rounding to two
decimal places,
is z=0.475−0.400.40(1−0.40)400‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ ≈3.06. Thus
the p-value is the area under the Standard Normal curve to the right of a z-score of
3.06.
From a lookup table of the area under the Standard Normal curve, the
corresponding area is then 1 - 0.999 = 0.001.
