MATH 225N 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.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
3.0 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999
Required p-value = 0.001
Explanation:
Formula to calculate the test statistic z is
z=((1−p)∗p)/np^−p where p^=x/n=190/400=0.475,p=0.40,n=400 →((1−0.4)∗0.4)/400
0.475−0.4 →0.0244950.075 ⇒3.06
P(z>3.06) = 1-P(z<3.06)
⇒ 1 - 0.999 [Find 3.0 in row and 0.06 in column in above table]
⇒ 0.001
Hence, p-value is 0.001
Determine the p-value for a hypothesis test for proportion
Question
A police officer claims that the proportion of accidents that occur in the daytime
(versus nighttime) at a certain intersection is 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:
Perfect. Your hard work is paying off 😀 Here are the steps needed to calculate
the p-value for a hypothesis test for a proportion:
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.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
3.0 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999
Required p-value = 0.001
Explanation:
Formula to calculate the test statistic z is
z=((1−p)∗p)/np^−p where p^=x/n=190/400=0.475,p=0.40,n=400 →((1−0.4)∗0.4)/400
0.475−0.4 →0.0244950.075 ⇒3.06
P(z>3.06) = 1-P(z<3.06)
⇒ 1 - 0.999 [Find 3.0 in row and 0.06 in column in above table]
⇒ 0.001
Hence, p-value is 0.001
Determine the p-value for a hypothesis test for proportion
Question
A police officer claims that the proportion of accidents that occur in the daytime
(versus nighttime) at a certain intersection is 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:
Perfect. Your hard work is paying off 😀 Here are the steps needed to calculate
the p-value for a hypothesis test for a proportion:
