Question 1

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 19%,and find a P-value of 0.17.Provide an appropriate conclusion.

Accepted Answer

There's a 17% chance that poll results could be just natural sampling variation rather than a real change in public opinion.

Question 2

The seller of a loaded die claims that it will favor 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.

Accepted Answer

There's a 1% chance that a fair die could randomly produce the results we observed,so there is strong evidence to conclude that the die is loaded.

Question 3

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose we claim that the current unemployment rate differs from the April 2011 unemployment rate.If we wish to support our claim,what are the null and alternative hypotheses? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

A

Question 4

A weight loss program provided a loss for 60% of its participants.The program leader decides to test a new weight loss strategy to see if it's better and gets a P-value of 0.21.Is it reasonable to conclude that the new strategy and the old one are equally effective?

Accepted Answer

The answer of A weight loss program provided a loss...

Question 5

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,and find a P-value of 0.005.Provide an appropriate conclusion
A)There is a 99.5% chance of no change in the chlorine proportion.
B)We can say there is a 0.5% chance of seeing a change in the chlorine proportions in the results we observed from natural sampling variation.We conclude the chlorine proportion is higher.
C)There is a 0.5% chance of no change in the chlorine proportion.
D)If the chlorine level is 0.4% mg/mL,then there is a 0.5% chance of seeing a sample chlorine level as high (or higher)than what we observed from natural sampling variation.There is no evidence of a higher chlorine proportion,but we cannot conclude the chlorine proportion is the same.
E)If the chlorine level is 0.4% mg/mL,then there is a 0.5% chance of seeing a sample chlorine level as high (or higher)than what we observed from natural sampling variation.There is very strong evidence the chlorine proportion is higher.

Accepted Answer

A P-value of 0.005 (or 0.5%) indicates that there is a very low probability of observing the sample results if the null hypothesis (no change in chlorine proportions) were true. This suggests strong evidence against the null hypothesis, implying that the chlorine proportion has likely increased.

Question 6

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?
A)If the percentage of obese Canadians has not changed,then there is a 2.8% chance of seeing the increase in the percentage of obese Canadians that we observed (or higher)from natural sampling variation.There is no evidence the percentage of obese Canadians has increased since 2004,but we cannot conclude the percentage hasn't increased.
B)There is a 97.2% chance that the percentage of obese Canadians has increased since 2004.
C)There is a 2.8% chance that the percentage of obese Canadians has increased since 2004.
D)If the percentage of obese Canadians has not changed,then there is a 2.8% chance of seeing the increase in the percentage of obese Canadians that we observed (or higher)from natural sampling variation.There is strong evidence that the percentage of obese Canadians has increased since 2004.
E)We can say there is a 2.8% chance that the percentage of obese Canadians has increased in the results we observed from natural sampling variation.We conclude that the percentage of obese Canadians has not increased since 2004.

Accepted Answer

The P-value of 0.028 indicates that if the percentage of obese Canadians had not changed since 2004, there is a 2.8% chance of observing the increase in the percentage of obese Canadians that we did from natural sampling variation. This is a low probability, and it gives us strong evidence to conclude that the percentage of obese Canadians has indeed increased since 2004. Therefore, the best choice is D, which correctly summarizes this interpretation.

Question 7

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose we claim that the current unemployment rate differs from the April 2011 unemployment rate.Statistics Canada claims that the current unemployment rate is lower than that of April 2011.To test this claim,a hypothesis test is conducted and yields a P-value turns out to be 0.04.Provide an appropriate conclusion.
A)If the current unemployment rate is 7.6%,there there is a 4% chance of seeing a sample unemployment rate as low (or lower)than what we observed from natural sampling variation.There is no evidence of that the unemployment rate decreased,but we can not conclude there is no change in the unemployment rate.
B)There is a 4% chance of no change in the unemployment rate.
C)There is a 96% chance of no change in the unemployment rate.
D)We can say there is a 4% chance of seeing a change in the unemployment rate in the results we observed from natural sampling variation.We conclude the Statistics Canada is correct and the unemployment rate has decreased.
E)If the current unemployment rate is 7.6%,there there is a 4% chance of seeing a sample unemployment rate as low (or lower)than what we observed from natural sampling variation.There is strong evidence that Statistics Canada is correct and the unemployment rate has decreased.

Accepted Answer

With a P-value of 0.04, we can conclude that there is a low probability of the observed result occurring by chance alone. Therefore, we reject the null hypothesis and accept the alternative hypothesis that the current unemployment rate is lower than that of April 2011. Additionally, there is strong evidence that Statistics Canada's claim is correct, and the unemployment rate has decreased.

Question 8

4% of trucks of a certain model have needed new engines after being driven between 0 and 100 kilometres.The manufacturer hopes that the redesign of one of the engine's components has solved this problem.

A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of 4% of trucks of a certain model...

Question 9

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.What are the null and alternative hypotheses? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A weight loss centre provided a loss...

Question 10

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 an appropriate hypothesis.What are the null and alternative hypotheses? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A city claims that 75% of all...

Question 11

A survey investigation whether the proportion of employees who commute by car to work is higher than it was five years ago finds a P-value of 0.009.Is it reasonable to conclude that more employees are commuting by car?

Accepted Answer

The answer of A survey investigation whether the proportion of...

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 more 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? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

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

Question 13

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 21%.They will use a follow-up poll to assess the ad's effectiveness.

A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A mayor is concerned about the percentage...

Question 14

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A new manager,hired at a large warehouse,was...

Question 15

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 reevaluates its retention rate and comes up with a P-value of 0.075.What is reasonable to conclude about the new programs?
A)There is a 7.5% chance of the new programs having no effect on retention.
B)If the new programs have no effect on the retention rate,then there is a 7.5% chance of seeing the increase in the retention rate that we observed (or higher)from natural sampling variation.We conclude the new programs are more effective.
C)If the new programs have no effect on the retention rate,then there is a 7.5% chance of seeing the increase in the retention rate that we observed (or higher)from natural sampling variation.There is suggestive but inconclusive evidence the new programs are more effective,but we cannot conclude the new programs have no effect on retention.
D)We can say there is a 7.5% chance of seeing the new programs having an effect on retention in the results we observed from natural sampling variation.We conclude the new programs are more effective.
E)There is a 92.5% chance of the new programs having no effect on retention.

Accepted Answer

A P-value of 0.075 indicates that there is a 7.5% chance of observing the increase in retention rate (or higher) due to natural sampling variation, if the new programs have no effect on retention. However, this does not provide conclusive evidence that the new programs are more effective. It only suggests that there may be some effect, but further investigation is needed to determine the extent of the effect and rule out other potential factors that may have contributed to the increase in retention rate. Therefore, option C is the most appropriate choice.

Question 16

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 and receives a P-value of 0.06.What is reasonable to conclude about the new strategy?
A)There is a 94% chance of the new program having no effect on employee attendance.
B)If the sick leave percentage has not changed,then there is a 6% chance of seeing the decrease in the sick leave percentage we observed (or lower)from natural sampling variation.We can conclude the new program is more effective.
C)There is a 6% chance of the new program having no effect on employee attendance.
D)We can say there is a 6% chance of seeing the new program having no effect on employee attendance in the results we observed from natural sampling variation.We conclude the new program is more effective.
E)If the sick leave percentage has not changed,then there is a 6% chance of seeing the decrease in the sick leave percentage we observed (or lower)from natural sampling variation.There is moderate evidence the new program is more effective,but we cannot conclude the program has no effect on employee attendance.

Accepted Answer

The answer of A new manager,hired at a large warehouse,was...

Question 17

Health Canada reports that,in 2005,85% of Canadians were satisfied with the health care services they received.Suppose you are now concerned that a smaller percentage of Canadians are satisfied with the health care services they received.If you want to justify your concerns,what are the null and alternative hypotheses? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Health Canada reports that,in 2005,85% of Canadians...

Question 18

In 2010,the proportion of employees at a large company who commuted to work by car was 8%.A current survey investigates whether the proportion of employees who commute by car to work is higher than it was in 2010.What are the null and alternative hypotheses? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of In 2010,the proportion of employees at a...

Question 19

At a local university,only 62% of the original freshman class graduated in four years.Has this percentage changed? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of At a local university,only 62% of the...

Question 20

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 an appropriate hypothesis.The P-value turns out to be 0.025.Provide an appropriate conclusion.
A)There is a 2.5% chance of no change in the proportion of housing that is 1500 sq.ft.
B)There is a 97.5% chance of no change in the proportion of housing that is 1500 sq.ft.
C)We can say there is a 2.5% chance of seeing a change in the proportion of housing that is 1500 sq.ft.in the results we observed from natural sampling variation.We conclude the tenants are correct and that the proportion of housing with 1500 square feet is less than 75%.
D)If 75% of all low income housing is 1500 sq.ft. ,then there is a 2.5% chance of seeing a sample proportion of such houses as low (or lower)than what we we observed from natural sampling variation.There is no evidence of that the proportion of housing is smaller than 1500 sq.ft. ,but we can not conclude there is no change in the proportion of housing that is 1500 sq.ft.
E)If 75% of all low income housing is 1500 sq.ft. ,then there is a 2.5% chance of seeing a sample proportion of such houses as low (or lower)than what we we observed from natural sampling variation.There is strong evidence the tenants are correct and that the proportion of housing with 1500 square feet is less than 75%.

Accepted Answer

The P-value of 0.025 indicates that if the true proportion were 75%, there is only a 2.5% chance of observing a sample proportion as extreme as the one found. This provides strong evidence against the null hypothesis, supporting the tenants' claim that the proportion is less than 75%.

Quiz 19: Testing Hypotheses About Proportions

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 19%,and find a P-value of 0.17.Provide an appropriate conclusion.

The seller of a loaded die claims that it will favor 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.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose we claim that the current unemployment rate differs from the April 2011 unemployment rate.If we wish to support our claim,what are the null and alternative hypotheses?

A weight loss program provided a loss for 60% of its participants.The program leader decides to test a new weight loss strategy to see if it's better and gets a P-value of 0.21.Is it reasonable to conclude that the new strategy and the old one are equally effective?

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,and find a P-value of 0.005.Provide an appropriate conclusion

4% of trucks of a certain model have needed new engines after being driven between 0 and 100 kilometres.The manufacturer hopes that the redesign of one of the engine's components has solved this problem.

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.What are the null and alternative hypotheses?

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 an appropriate hypothesis.What are the null and alternative hypotheses?

A survey investigation whether the proportion of employees who commute by car to work is higher than it was five years ago finds a P-value of 0.009.Is it reasonable to conclude that more employees are commuting by car?

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 21%.They will use a follow-up poll to assess the ad's effectiveness.

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?

In 2010,the proportion of employees at a large company who commuted to work by car was 8%.A current survey investigates whether the proportion of employees who commute by car to work is higher than it was in 2010.What are the null and alternative hypotheses?

At a local university,only 62% of the original freshman class graduated in four years.Has this percentage changed?

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 an appropriate hypothesis.The P-value turns out to be 0.025.Provide an appropriate conclusion.