Exam 18: 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 or higher.Suppose you believe that the percentage of obese Canadians has increased since 2004 and wish to test your belief.What are the null and alternative hypotheses?

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 $\alpha = 0.01$ and the unemployment rate is currently 6.1%,what is the power of the test?

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 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?

A researcher has tested the difference between the means of a treatment group and a placebo group.He found a P-value of 0.034.Interpret the p-value and provide an appropriate conclusion at α = 0.01.

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? State the critical value required to perform an appropriate hypothesis test using α = 0.05.

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?

Farmers concerned with the effect of snowfall levels on their crops found that there wasn't evidence of a decrease in crop growth.They based this conclusion on a test using α = 0.10.Would they have made the same decision at α = 0.05 and α = 0.01?

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?

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? 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 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?

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? State the critical value required to perform an appropriate hypothesis test using α = 0.10.

The mayor's disapproval rating was previously 13%.After a political ad campaign for a city's mayor,pollsters check the disapproval ratings.They test the hypothesis that the ads produced no change against the alternative that the ratings are now below 13%,and find a P-value of 0.11.Provide an appropriate conclusion using α = 0.10.

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 intact,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.

After performing a hypothesis test,a first year statistics student found a p-value of 0.047.In their conclusion,they state that,given the data,there is a 4.7% chance the null hypothesis is true.And thus,they decide to reject the null hypothesis.What is wrong with their conclusion?

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

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.Suppose you wish to conduct a test to determine if the current unemployment rate is lower than that of April 2011.Identify the Type II error in this context.

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.

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 a random sample size of 120 and found 1500 sq.ft.housing at 66%.State the critical value required to perform an appropriate hypothesis test using α = 0.001.