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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
Great work! That's correct.
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.
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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.
Well done! You got it right.
3.32 The proportion of successes is p̂ =221250=0.884.
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
Question
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