MATH 225N Week 7 Assignment Conduct a Hypothesis Test for Proportion – P-Value Approach
Question
A college administrator claims that the proportion o
... [Show More] f 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)/4000.475−0.4 →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
For this example, the test is a two tailed test and the test statistic, rounding to two decimal places, is z=0.312−0.350.35(1−0.35)500‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√≈1.78.
Thus the p-value is the area under the Standard Normal curve to the left of a z-score of -1.78, plus the area under the Standard Normal curve to the right of a z-score of 1.78
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037
From a lookup table of the area under the Standard Normal curve, the corresponding area is then 2(0.038) = 0.076.
Make a conclusion and interpret the results for a hypothesis test for proportion using the P-Value Approach
Question
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.
The following is the setup for this hypothesis test:
H0:p=0.80
Ha:p>0.80
In this example, the p-value was determined to be 0.944.
Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)
Correct! You nailed it. 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.
Make a conclusion and interpret the results for a hypothesis test for proportion using the P-Value Approach
Question
A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts.
The following is the setup for this hypothesis test:
H0:p=0.65
Ha:p<0.65
In this example, the p-value was determined to be 0.277.
Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) Perfect. Your hard work is paying off 😀 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 = 0.277. 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.
Determine the p-value for a hypothesis test for proportion
Question
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.
The following is the setup for this hypothesis test:
H0:p=0.80
Ha:p>0.80
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: Great work! That's correct. Correct answers:
• P-value=0.944
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=0.755−0.800.80(1−0.80)200‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√≈−1.59.
Thus the p-value is the area under the Standard Normal curve to the right of a z-score of -1.59. From a lookup table of the area under the Standard Normal curve, the corresponding area is then 1 - 0.056 = 0.944.
Determine the p-value for a hypothesis test for proportion
Question
A business owner claims that the proportion of take out orders is greater than 25%. To test this claim, the owner checks the next 250 orders and determines that 60 orders are take out orders.
The following is the setup for this hypothesis test:
H0:p=0.25
Ha:p>0.25
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 😀 Correct answers:
• P-value=0.643
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=0.24−0.250.25(1−0.25)250‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√≈−0.37.
Thus the p-value is the area under the Standard Normal curve to the right of a z-score of -0.37. From a lookup table of the area under the Standard Normal curve, the corresponding area is then 1 - 0.357 = 0.643
Make a conclusion and interpret the results for a hypothesis test for proportion using the P-Value Approach
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
In this example, the p-value was determined to be 0.075. 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 reject 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 = 0.075. 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.Yes that's right. Keep it up!
Make a conclusion and interpret the results for a hypothesis test for proportion using the P-Value Approach
Question
A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. .
The following is the setup for this hypothesis test:
H0:p=0.12
Ha:p≠0.12
In this example, the p-value was determined to be 0.124.
Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) Perfect. Your hard work is paying off 😀 Correct answer:
The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to reject 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 = 0.124. 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. [Show Less]