Question 1

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 4%.What are the null and alternative hypotheses?

Accepted Answer

A) H0: p = 0.04 HA: p  0.04 
C) H0: p  0.04 
E) H0: p > 0.04 HA: p = 0.04 
A) H0: p = 0.04 HA: p  0.04 
C) H0: p  0.04 
E) H0: p > 0.04 HA: p = 0.04 A

Question 2

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?

Accepted Answer

A) H0: p = 0.75 HA: p  0.75 HA: p  0.75 
A) H0: p = 0.75 HA: p  0.75 HA: p  0.75 A

Question 3

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 α = 0.05 and the unemployment rate is currently 6.1%,what is the power of the test?

Accepted Answer

A) 0.8547 
B) 0.0104 
C) 0.5636 
D) 0.9896 
E) 0.4364 
A) 0.8547 
B) 0.0104 
C) 0.5636 
D) 0.9896 
E) 0.4364 C

Question 4

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?

Accepted Answer

A) H0: p > 0.26 HA: p  0.26 
E) H0: p = 0.26 HA: p ≠ 0.26 
A) H0: p > 0.26 HA: p  0.26 
E) H0: p = 0.26 HA: p ≠ 0.26

Question 5

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) The error of failing to accept the claim that the true proportion is at least 3% when it is actually less than 3%. 
B) The error of rejecting the claim that the true proportion is at least 3% when it really is at least 3%. 
C) The error of failing to reject the claim that the true proportion is at least 3% when it is actually less than 3%. 
D) The error of rejecting the claim that the true proportion is less than 3% when it really is less than 3%. 
E) The error of accepting the claim that the true proportion is at least 3% when it really is at least 3%. 
A) The error of failing to accept the claim that the true proportion is at least 3% when it is actually less than 3%. 
B) The error of rejecting the claim that the true proportion is at least 3% when it really is at least 3%. 
C) The error of failing to reject the claim that the true proportion is at least 3% when it is actually less than 3%. 
D) The error of rejecting the claim that the true proportion is less than 3% when it really is less than 3%. 
E) The error of accepting the claim that the true proportion is at least 3% when it really is at least 3%.

Question 6

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 $\alpha = 0.05$ and the unemployment rate is currently 7.1%,what is the power of the test?

Accepted Answer

A) 0.1401 
B) 0.1326 
C) 0.8674 
D) 0.9215 
E) 0.8599 
A) 0.1401 
B) 0.1326 
C) 0.8674 
D) 0.9215 
E) 0.8599

Question 7

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? Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

@#IMG-DLM& : p = 0.15; @#IMG-DLM& : p < 0.15; z = -4.21,p =

Question 8

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.What are the null and alternative hypotheses?

Accepted Answer

A) H0: p > 0.08 HA: p 0.08 D) H0: p = 0.08 HA: p ≠ 0.08 E) H0: p < 0.08 HA: p = 0.08 A) H0: p > 0.08 HA: p 0.08 D) H0: p = 0.08 HA: p ≠ 0.08 E) H0: p < 0.08 HA: p = 0.08

Question 9

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.

Accepted Answer

@#IMG-DLM& : p = 0.38; @#IMG-DLM& : p < 0.38; z = -2.82,p =

Question 10

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 $\alpha = 0.05 .$ Would he have made the same decision at $\alpha = 0.10$ and $\alpha = 0.01 ?$

Accepted Answer

α = 0.10: Yes.The P-value is <

Question 11

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%.Test an appropriate hypothesis using α = 0.01 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

@#IMG-DLM& : p = 0.75; @#IMG-DLM& : p < 0.75; z = -2.28; P-v

Question 12

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.Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

@#IMG-DLM& : p = 0.72; @#IMG-DLM& : p > 0.72; z = 1.58; P-va

Question 13

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.

Accepted Answer

A) -1.645 
B) 1.96 
C) 2.576 
D) 2.326 
E) 1.645 
A) -1.645 
B) 1.96 
C) 2.576 
D) 2.326 
E) 1.645

Question 14

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

A) The error of rejecting the claim that the true proportion is less than 5% when it really is less than 5%. 
B) The error of failing to reject the claim that the true proportion is at least 5% when it is actually less than 5%. 
C) The error of accepting the claim that the true proportion is at least 5% when it really is at least 5%. 
D) The error of rejecting the claim that the true proportion is at least 5% when it really is at least 5%. 
E) The error of accepting the claim that the true proportion is at least 5% when it is actually less than 5%. 
A) The error of rejecting the claim that the true proportion is less than 5% when it really is less than 5%. 
B) The error of failing to reject the claim that the true proportion is at least 5% when it is actually less than 5%. 
C) The error of accepting the claim that the true proportion is at least 5% when it really is at least 5%. 
D) The error of rejecting the claim that the true proportion is at least 5% when it really is at least 5%. 
E) The error of accepting the claim that the true proportion is at least 5% when it is actually less than 5%.

Question 15

Historical data showed that 24.3% of elementary students performed below their grade level in math.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 showed that the percentage of students who did not attain the grade level standard was reduced from 24.3% to 18.5%.This resulted in a P-Value of 0.047 for the test.Interpret the p-value and provide an appropriate conclusion at α = 0.05.

Accepted Answer

There is only a 4.7% chance of seeing a

Question 16

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) The firm concludes that the proportion of housing less than 1500 sq.ft.is smaller,but in fact there is no change in the proportion. 
B) The product of the firm's sample size and sample proportion was less than 10. 
C) The firm sampled all low income houses. 
D) The firm concludes that the proportion of housing this size is rising since the majority of housing can only increase. 
E) The firm shows there in no change in the proportion of housing this size,but in fact the proportion of houses less than 1500 sq.ft.is smaller. 
A) The firm concludes that the proportion of housing less than 1500 sq.ft.is smaller,but in fact there is no change in the proportion. 
B) The product of the firm's sample size and sample proportion was less than 10. 
C) The firm sampled all low income houses. 
D) The firm concludes that the proportion of housing this size is rising since the majority of housing can only increase. 
E) The firm shows there in no change in the proportion of housing this size,but in fact the proportion of houses less than 1500 sq.ft.is smaller.

Question 17

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

A) 0.008 
B) 0.90 
C) 0.10 
D) 0.92 
E) 0.08 
A) 0.008 
B) 0.90 
C) 0.10 
D) 0.92 
E) 0.08

Question 18

Researchers concerned with the effect of loud music on teenagers' hearing found that there wasn't evidence of a higher hearing loss among teenagers who frequently attended rock concerts.They based this conclusion on a test using α = 0.05.Would they have made the same decision at α = 0.10 and α = 0.01?

Accepted Answer

At α = 0.10 they reach the dec

Question 19

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

A) The error of rejecting the claim that the true proportion is at most 6.4% when it really is at most 6.4%. 
B) The error of accepting the claim that the true proportion is more than 6.4% when it really is more than 6.4%. 
C) The error of rejecting the claim that the true proportion is more than 6.4% when it really is more than 6.4%. 
D) The error of failing to accept the claim that the true proportion is at most 6.4% when it is actually more than 6.4%. 
E) The error of failing to reject the claim that the true proportion is at most 6.4% when it is actually more than 6.4%. 
A) The error of rejecting the claim that the true proportion is at most 6.4% when it really is at most 6.4%. 
B) The error of accepting the claim that the true proportion is more than 6.4% when it really is more than 6.4%. 
C) The error of rejecting the claim that the true proportion is more than 6.4% when it really is more than 6.4%. 
D) The error of failing to accept the claim that the true proportion is at most 6.4% when it is actually more than 6.4%. 
E) The error of failing to reject the claim that the true proportion is at most 6.4% when it is actually more than 6.4%.

Question 20

Have harsher laws decreased the number of drivers under the influence? Data from Friday and Saturday evening traffic were collected and compared with similar data from ten years ago.The P-value of the study was $\mathrm { P } = 0.23 .$ Interpret the p-value and provide an appropriate conclusion at $\alpha = 0.05$ .

Accepted Answer

If harsher laws have not made a differen

Exam 18: More About Tests

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 4%.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 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?

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.

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.What are the null and alternative hypotheses?

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.

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.

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 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.

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