Question 1

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?

Accepted Answer

The answer of According to the 2004 Canadian Community Health...

Question 2

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.

Accepted Answer

A Type II error occurs when we fail to reject a null hypothesis that is actually false. In this context, the null hypothesis would be that the current unemployment rate is not lower than that of April 2011. So, if we commit a Type II error, we would conclude that there is no change in unemployment (i.e., fail to reject the null hypothesis) even though the unemployment rate is actually decreasing. Option B is the only choice that describes this situation.

Question 3

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.

Accepted Answer

The answer of A company is willing to renew its...

Question 4

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.

Accepted Answer

For a one-tailed test with α = 0.001, the critical value corresponds to the z-score that has 0.001 area in the tail. The negative sign indicates the tenants believe the proportion is smaller, so -3.09 is the correct critical value for α = 0.001 on the left tail of the distribution.

Question 5

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.

Accepted Answer

A Type II error occurs when the null hypothesis is not rejected when it is false. In this context, it means failing to detect an increase in commuting by car when there actually is an increase.

Question 6

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.

Accepted Answer

A Type I error occurs when the null hypothesis is true, but is incorrectly rejected. In this context, the null hypothesis is that 75% of all low income housing is 1500 sq.ft. A Type I error would occur if the firm concludes the proportion is smaller when, in fact, it is not.

Question 7

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.

Accepted Answer

The critical value for a one-tailed test with α = 0.05 is 1.645.

Question 8

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.

Accepted Answer

A Type I error occurs when a true null hypothesis is rejected. In this case, the null hypothesis would be that the percentage of obese Canadians has not decreased since 2004. If the researcher concludes that the percentage of obese Canadians has decreased, but in fact it has stayed the same or increased, this would be a Type I error. Option B describes this scenario. Options A, C, and D do not describe a Type I error. Option E is incorrect because Type I errors can occur in any hypothesis testing situation.

Question 9

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?

Accepted Answer

The answer of According to the 2004 Canadian Community Health...

Question 10

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.

Accepted Answer

A Type I error in this situation would be concluding that the percentage of satisfied Canadians has decreased, when it has actually stayed the same or increased. This is because the null hypothesis in this case is that the percentage of satisfied Canadians has not decreased, and a Type I error would mean rejecting this null hypothesis when it is actually true.

Question 11

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.

Accepted Answer

Type II error is failing to reject a false null hypothesis. In this context, the null hypothesis would be that the proportion who suffer from professional problems due to extreme shyness is equal to or less than 6.4%. The psychologist claims that the true proportion is greater than 6.4%, so if we fail to reject the null hypothesis (i.e. we do not find enough evidence to conclude that the true proportion is greater than 6.4%), it would be a Type II error. Choice E is the only one that describes this error.

Question 12

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?

Accepted Answer

The answer of According to the 2004 Canadian Community Health...

Question 13

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.

Accepted Answer

A Type I error is the error of rejecting a null hypothesis when it is actually true. In this context, the null hypothesis is that the true proportion of male fireflies unable to produce light due to a genetic mutation is at least 3%. The article claims that the proportion is fewer than 3%. If the true proportion is actually at least 3% but the article claims that it is fewer than 3%, then the article is making a Type I error by falsely rejecting the null hypothesis. Therefore, option B is the correct answer.

Question 14

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?

Accepted Answer

Power of a hypothesis test is the probability of correctly rejecting a false null hypothesis. 
Since the probability of Type II error is 0.08, the power of the test is 1 - 0.08 = 0.92. Therefore, the answer is D, 0.92.

Question 15

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 24.8%,what is the power of the test?

Accepted Answer

The answer of According to the 2004 Canadian Community Health...

Question 16

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.Identify the Type I error in this context.

Accepted Answer

A Type I error occurs when the null hypothesis is rejected when it is actually true. In this context, the null hypothesis would be that the new programs did not increase the retention rate. If the university concludes that retention is on the rise but in fact the new programs did not help retention, then it would be committing a Type I error by rejecting the null hypothesis when it is actually true.

Question 17

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.

Accepted Answer

The Type I error in this context would be if the centre concludes that the new weight loss strategy is effective at increasing the proportion of participants who lose weight, when in reality it does not help with weight loss. This is a Type I error because it would be a false positive, meaning the centre would falsely conclude that the new strategy is effective when it is not. Option B describes this scenario, making it the correct choice. The other options either do not relate to Type I error or are incorrect explanations of the situation.

Question 18

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.

Accepted Answer

To test the effectiveness of the new curriculum, a hypothesis test for a proportion can be used. Given a significance level (α) of 0.01 for a two-tailed test, the critical value corresponds to the z-score that captures the central 99% of the normal distribution. The correct critical value for a two-tailed test at α = 0.01 is -2.326 or 2.326, but since only negative values are listed, -2.326 is the correct choice. This value is used to determine the rejection regions for the null hypothesis.

Question 19

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO,p,is less than 5%.Identify the Type II error in this context.

Accepted Answer

In this context, a Type II error would occur if the researcher fails to reject the null hypothesis that the true proportion is at least 5% (i.e. the researcher cannot conclude that the proportion is less than 5%) when it is actually less than 5%. This means that the researcher would not have enough evidence to support their claim that the proportion of Americans who have seen a UFO is less than 5%.

Question 20

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.

Accepted Answer

The answer of A Math professor has observed over several...

Quiz 18: More About Tests

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.

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 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.

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.

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?

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.Identify the Type I error in this context.

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.

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO,p,is less than 5%.Identify the Type II error in this context.