Q1
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?
Ans:
Although the proportion follows a binomial model with two independent outcomes and the data are selected at random, the number of successes and the number of failures are not both greater than or equal to 5.
Although the proportion follows a binomial model with two independent outcomes and the number of successes and the number of failures are both greater than or equal to 5, the data are not selected at random.
Although the data are selected at random and the number of successes and the number of failures are both greater than or equal to 5, the proportion does not follow a binomial model.
All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.94Ha:p≠0.94.
All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.94Ha:p>0.94.
All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.94Ha:p<0.94
Q2
A hospital administrator claims that the proportion of knee surgeries that are successful is 87%. To test this claim, a random sample of 450 patients who underwent knee surgery is taken and it is determined that 371 of these patients had a successful knee surgery operation.
The following is the setup for this hypothesis test:
{H0:p=0.87Ha:p≠0.87
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
Q3
A local cable company claims that the proportion of people who have Internet access is less than 63%. To test this claim, a random sample of 800 people is taken and its determined that 454 people have Internet access.
The following is the setup for this hypothesis test:
{H0:p=0.63Ha:p<0.63
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
Q4
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?
Ans:
Q5
A researcher claims that the proportion of college students who plan to participate in community service after graduation is greater than 35%. To test this claim, a survey asked 500 randomly selected college students if they planned to perform community service after graduation. Of those students, 195 indicated they planned to perform community service.
The following is the setup for the hypothesis test:
{H0:p=0.35Ha:p>0.35
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
Q6
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.
Q7
Colin is a student in a statistics course looking to show whether the proportion of games played that are won by the visiting team in a certain professional lacrosse league is 50%. Colin randomly selects 83 games from the past few seasons and finds that 37 of the games were won by the visiting team. What are the null and alternative hypotheses for this hypothesis test?
Ans:
Q8
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?
Ans:
Solution
Q1
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?
Ans:
Although the proportion follows a binomial model with two independent outcomes and the data are selected at random, the number of successes and the number of failures are not both greater than or equal to 5.
Although the proportion follows a binomial model with two independent outcomes and the number of successes and the number of failures are both greater than or equal to 5, the data are not selected at random.
Although the data are selected at random and the number of successes and the number of failures are both greater than or equal to 5, the proportion does not follow a binomial model.
All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.94Ha:p≠0.94.
All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.94Ha:p>0.94.
All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.94Ha:p<0.94…………please follow the link below to access all answers at $5 only
