Exam 20: More About Tests

A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,the university reevaluated its retention rate using a random sample of 352 students and retained 18 students.Should the university continue its new programs? Test an appropriate hypothesis using α = 0.10 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese;that is,they had a body mass index (BMI)of 30 more higher.Suppose you believe that the percentage of obese Canadians has increased since 2004.To test your belief take a random sample of 1000 Canadians.If you plan to perform the test at α = 0.05 and the true percentage of obese Canadians is currently 25.9%,what is the power of the test?

A Science professor has observed over several years that about 15% of the students who initially major in Science drop out of the program after their freshman year.The department head suggested making the curriculum easier by taking a couple of 300 level courses out of the requirements.With the new curriculum in tact,590 began their freshman year as Science majors and only 52 dropped out of the program.Should the college continue with the easier curriculum? State the critical value required to perform an appropriate hypothesis test using α = 0.01.

An entomologist writes an article in a scientific journal which claims that fewer than 3% of male fireflies are unable to produce light due to a genetic mutation.Identify the Type I error in this context.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.To test their belief,they plan to take a random sample size of 1000 people.If they plan to perform the test at α = 0.05 and the unemployment rate is currently 6.1%,what is the power of the test?

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.To test their belief,they plan to take a random sample size of 1000 people.If they plan to perform the test at α = 0.05 and the unemployment rate is currently 7.1%,what is the power of the test?

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 4%.What are the null and alternative hypotheses?

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese;that is,they had a body mass index (BMI)of 30 more higher.Suppose you believe that the percentage of obese Canadians has increased since 2004.To test your belief take a random sample of 1000 Canadians.If you plan to perform the test at α = 0.01 and the true percentage of obese Canadians is currently 24.8%,what is the power of the test?

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.To test their belief,they plan to take a random sample size of 1000 people.If they plan to perform the test at α = 0.10 and the unemployment rate is currently 6.1%,what is the power of the test?

A professional basketball player with a poor free throw percentage gets a personal coach to help him increase his percentage.He tells his coach that he has raised his proficiency from 40% to 60%.To see whether the athlete has improved,the coach asks the athlete to take ten shots.He hits 7 out of 10.If the player really can hit 60% now,and it takes at least 7 out of 10 successful shots to convince the coach,what's the power of the test?

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy on a random sample size of 140 and found weight loss in 78% of the participants.Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

An entomologist writes an article in a scientific journal which claims that fewer than 29% of male fireflies are unable to produce light due to a genetic mutation.What are the null and alternative hypotheses?

A new manager,hired at a large warehouse,was told to reduce the 26% employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager decides to test the new program to see if it's better.What are the null and alternative hypotheses?

A psychologist claims that more than 6.4% of the population suffers from professional problems due to extreme shyness.Identify the Type II error in this context.

A manager of a large company believes that 95% of her employees use their 40 hours of weekly work time productively.A random survey given to some of the employees found that only 92.7% of her employees used their time productively.A statistician rejected the 95% hypothesis with a P-value of P = 0.021.

Researchers concerned with the effect of loud music on teenagers' hearing found that there wasn't evidence of a higher hearing loss among teenagers who frequently attended rock concerts.They based this conclusion on a test using α = 0.05.Would they have made the same decision at α = 0.10 and α = 0.01?

A company is willing to renew its publishing contract with a popular statistics book author only if he can prove that his book can sell to more than 22% of the entire statistics market.The publishing company contacts 5000 statistics professors at random and only 1050 professors were interested in the book.Should the company renew the contract? Should the company renew the contract? State the critical value required to perform an appropriate hypothesis test using α = 0.01.

Five years ago,a company found that 8% of its employees commuted to work by car.A survey investigates whether the current proportion of employees who commute by car to work is higher than it was five years ago.What are the null and alternative hypotheses?

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese;that is,they had a body mass index (BMI)of 30 more higher.Suppose you believe that the percentage of obese Canadians has increased since 2004 and wish to test your belief.You hire an independent agency to conduct a hypothesis test and they come up with a P-value of 0.028.What is reasonable to conclude using α = 0.05?

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy to see if it's better and receives a P-value of 0.23.What is reasonable to conclude about the new strategy using α = 0.10?