MATH 225N Week 7 Assignment / MATH225 Week 7 Assignment (Version 2, New-2021): Conduct a Hypothesis Test for Proportion P-Value Approach :Chamberlain College of Nursing (ANSWERS VERIFIED)

MATH225 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:

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