Exam 20: More About Tests

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 = 0.10 and the true percentage of obese Canadians is currently 25.9%,what is the power of the test?

The management of a water park has concerns about the chlorine level of 0.4% mg/mL increasing to an unsafe level.The management tests the hypothesis that the park's chlorine proportions have remained the same,hat are the null and alternative hypotheses?

A dentist that is developing detection devices to search for tooth decay has concluded that his new device is significantly better than taking X-rays.He made this decision using α = 0.05.Would he have made the same decision at α = 0.10 and α = 0.01?

Consider a hypothesis test where the probability of a Type I error is 0.10 and the probability of a Type II error is 0.08.What is the power of the test?

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.A test on employee commuting by car was done on a random sample of 1000 employees,and found car commuting to be 12%.Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A Math professor has observed over several years that about 38% of the students who initially major in Math 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 intact,207 began their freshman year as Math majors and only 59 dropped out of the program.Should the college continue with the easier curriculum? Test an appropriate hypothesis using α = 0.05 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 decreased since 2004 and wish to test your belief.A current survey of 1000 random Canadians found that 219 were obese.State the critical value required to perform an appropriate hypothesis test using α = 0.05.

A diesel engine company that is developing a new engine has concluded that the updated engine provides better fuel economy than the current engine.They made this decision using α = 0.01.Would they have made the same decision at α = 0.10 and α = 0.05?

Health Canada reports that,in 2005,85% of Canadians were satisfied with the health care services they received.Suppose you wish to conduct a hypothesis test to determine if there is now a smaller percentage of Canadians are satisfied with the health care services they received.Identify the Type I error in this context.

A company has surveyed a sample of its employees to find out how many might take advantage of a weight loss program.The table below shows the results.For which of the groups could we use our methods of inference to determine a 95% confidence interval for the proportion of employees who would be willing to participate in the program?

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.State the critical value required to perform an appropriate hypothesis test using 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? Test an appropriate hypothesis using α = 0.01 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test the hypothesis.Identify the Type I error in this context.

A mayor is concerned about the percentage of city residents who express disapproval of his job performance.His political committee pays for a newspaper ad,hoping that it will keep the disapproval rate below 22%.They will use a follow-up poll to assess the ad's effectiveness.

A new math program may reduce the number of elementary students who perform below their grade level.The company that developed this program supplied materials and teacher training to 3000 children and 400 teachers.Statistical analysis of the results showed that the percentage of students who did not attain the grade level standard was reduced from 24.3% to 18.5%.The hypothesis that the new reading program did not produce improvement was rejected with a P-value of 0.047.

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.A test on employee commuting by car was done on a random sample of 1000 employees,and found car commuting to be 12%.State the critical value required to perform an appropriate hypothesis test using α = 0.001.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada wishes to determine if the current unemployment rate differs from that of April 2011.To perform a hypothesis test,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 8.1%,what is the power of the test?

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 24.8%,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 70% to 90%.To see whether the athlete has improved,the coach asks the athlete to take 10 shots.He hits 10 out of 10.Suppose the athlete really is no better than before (still a 70% shooter).What's the probability that he could hit at least 10 out of 10 shots anyway?

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.A current survey of 1000 random Canadians found that 245 were obese.Test an appropriate hypothesis using α = 0.10 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.