Exam 18: More About Tests

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 $\alpha = 0.10$ and the unemployment rate is currently 6.1%,what is the power of the test?

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.

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 or higher.Suppose you believe that the percentage of obese Canadians has decreased since 2004 and wish to test your belief.Identify the Type I error in this context.

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.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose you wish to conduct a test to determine if the current unemployment rate differs from that of April 2011.What are the null and alternative hypotheses?

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 conducts a hypothesis test to determine if the retention rate has increased and obtains a P-value of 0.075.What is reasonable to conclude about the new programs using α = 0.05?

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 or higher.Suppose you believe that the percentage of obese Canadians has increased since 2004 and wish to test your belief.A current survey in 2014 of 1000 random Canadians resulted in P-value of 0.028 for your test.What is reasonable to conclude using α = 0.05?

The seller of a loaded die claims that it will favour the outcome 6.We don't believe that claim,and roll the die 350 times to test an appropriate hypothesis.Our P-value turns out to be 0.01.Provide an appropriate conclusion using α = 0.05.

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.Identify the Type II error in this context.

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 or higher.Suppose you believe that the percentage of obese Canadians has increased since 2004 and wish to test your belief.A current survey in 2014 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.

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%.You wish to know if the current unemployment rate differs from that of April 2011.You take a random sample size of 1000 and found unemployment at 6.1%.State the critical value required to perform an appropriate hypothesis test 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.Identify the Type I error in this context.

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 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 carried out a test and a P-value of 0.021.Interpret the p-value and provide an appropriate conclusion at α = 0.05.

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 or 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?

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 or higher.Suppose you believe that the percentage of obese Canadians has decreased since 2004 and wish to test your belief.A current survey in 2014 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 company is willing to renew its publishing contract with a popular calculus book author only if he can prove that his book can sell to more than 15% of the entire calculus market.The publishing company contacts 3000 calculus professors at random and only 420 professors were interested in the book.Should the company renew the contract? State the critical value required to perform an appropriate hypothesis test using α = 0.05.

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.What are the null and alternative hypotheses?

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.