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MATH 225N Week 7 Assignment- 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?{H0:p=0.06Ha:p>0.06
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. {H0:p=0.06Ha:p>0.06
Compute the value of the test statistic (z-value) for a hypothesis test for proportion
Question
A college professor claims that the proportion of students passing a statistics course is 80%. To test this claim, a random sample of 250 students who previously took the course is taken and it is determined that 221 students passed the course. Stuvia.com - The Marketplace to Buy and Sell your Study Material
The following is the setup for this hypothesis test:
H0:p = 0.80
Ha:p ≠ 0.80
Find the test statistic for this hypothesis test for a proportion and round your answer to 2 decimal places.
The test statistic is calculated as follows:
z=p̂ −p0p0⋅(1−p0)n√
z=0.884−0.800.80⋅(1−0.80)250√
z≈3.32
Compute the value of the test statistic (z-value) for a hypothesis test for proportion
Question
A researcher is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 92 people are unemployed.
The following is the setup for this hypothesis test:
{H0:p=0.05Ha:p<0.05
Find the test statistic for this hypothesis test for a proportion. Round your answer
to 2 decimal places. Test_Statistic=2.01 Great work! That's correct.
Identify the null and alternative hypotheses for an experiment with one population proportion
QuestionWell done! You got it right.
3.32The proportion of successes is p̂ =221250=0.884.
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