**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:

*H*0:*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.

**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.

# 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?

# Question

An airline company claims in a recent advertisement that more than 94% of passenger luggage that it lost is recovered and reunited with the customer within 1 day. Hunter is a graduate student studying statistics. For a research project, Hunter wants to find out whether there is convincing evidence in support of the airline company’s claim. He randomly selects 315 passengers of the airline whose luggage was lost by the airline and found that 276 of those passengers were reunited with their luggage within 1 day. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test?

# Question

Kylie works for a large nursery and is investigating whether to use a new brand of seeds. The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. She will change over to this new brand unless the actual germination rate is less than what is advertised. Kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. She finds that 70 of those seeds germinated. What are the null and alternative hypotheses for this hypothesis test?

# Question

A politician recently made the claim that 47% of taxpayers from a certain region do not pay any income taxes. Makayla is a journalist for an online media company and is testing the politician’s claim for an op-ed. She randomly selects 159 taxpayers from the region to conduct a survey and finds that 73 of them do not pay any income taxes. What are the null and alternative hypotheses for this hypothesis test?

**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:

{H0:p=0.40Ha:p>0.40

Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

**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.

# Solution:

# Question

Kylie works for a large nursery and is investigating whether to use a new brand of seeds. The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. She will change over to this new brand unless the actual germination rate is less than what is advertised. Kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. She finds that 70 of those seeds germinated. What are the null and alternative hypotheses for this hypothesis test?

Answer: H0:p=0.93 Ha:p<0.93

# Question

A politician recently made the claim that 47% of taxpayers from a certain region do not pay any income taxes. Makayla is a journalist for an online media company and is testing the politician’s claim for an op-ed. She randomly selects 159 taxpayers from the region to conduct a survey and finds that 73 of them do not pay any income taxes. What are the null and alternative hypotheses for this hypothesis test?

Answer: H0:p=0.47 Ha:p≠0.47

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