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.
, 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
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.
, 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
