MATH 225N Week 7 Assignment 2020 - Developing Hypothesis and understanding Possible Conclusion for Proportions
Identify the null and alternative hypotheses for an experiment with one population proportion
Question
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MATH 225N Week 7 Assignment 2020 - Developing Hypothesis and understanding Possible Conclusion for Proportions
Identify the null and alternative hypotheses for an experiment with one population proportion
Question
Devin is a researcher for a pharmaceutical company testing whether a new prescription pain medication causes patients to develop nausea. The medication would have to be scrapped if more than 6% of patients who take the medication develop nausea on a regular basis. Devin randomly selected 461 patients for a clinical trial of the medication and found that 27 of the patients developed nausea on a regular basis. What are the null and alternative hypotheses for this hypothesis test?
First verify whether all of the conditions have been met. Let p be the population proportion for patients taking the medication who develop nausea on a regular basis.
1. Since there are two independent outcomes for each trial, the proportion follows a binomial model.
2. The question states that the sample was collected randomly.
3. The expected number of successes, np=27.66, and the expected number of failures, nq=n(1−p)=433.34, are both greater than or equal to 5.
Since Devin is trying to determine whether more than 6% of the patients taking the medication develop nausea on a regular basis, the null hypothesis is that p is equal to 0.06 and the alternative hypothesis is that p is greater than 0.06. The null and alternative hypotheses are shown below.
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{H0:p=0.47Ha:p≠0.47
Compute the value of the test statistic (z-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:
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Correct answers:
The proportion of successes is p̂ =190400=0.475.
The test statistic is calculated as follows:
Compute the value of the test statistic (z-value) for a hypothesis test for proportion
Question
A researcher claims that the proportion of people who are right-handed is greater than 70%. To test this claim, a random sample of 600 people is taken and its determined that 410 people are right handed.
The following is the setup for this hypothesis test:
{H0:p=0.70Ha:p>0.70
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Correct answers:
Test_Statistic=−0.89 Well done! You got it right.
The proportion of successes is p̂ =410600=0.683.
The test statistic is calculated as follows:
z=p̂ −p0p0⋅(1−p0)n‾‾‾‾‾‾‾√
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