Question 1

An airline's public relations department says that the airline rarely loses passengers' luggage.It further claims that on those occasions when luggage is lost,92% is recovered and delivered to its owner within 24 hours.A consumer group who surveyed a large number of air travelers found that only 145 out of 165 people who lost luggage on that airline were reunited with the missing items by the next day.Does this cast doubt on the airline's claim? Use a calculator to find z-scores and P-values.

Accepted Answer

The answer of An airline's public relations department says that...

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

The answer of The seller of a loaded die claims...

Question 3

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 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

A)

: p = 0.75;

: p ≠ 0.75;z = -2.32;P-value = 0.0204.This data shows strong evidence that the proportion of 1500 sq.ft.housing is less than 75% 
B)

: p = 0.75;

: p  0.75;z = -2.32;P-value = 0.9898.This data shows no evidence that the proportion of 1500 sq.ft.housing is less than 75% 
D)

: p = 0.75;

: p > 0.75;z = 2.32;P-value = 0.9898.This data shows strong evidence that the proportion of 1500 sq.ft.housing is less than 75% 
E)

: p = 0.75;

: p < 0.75;z = -2.28;P-value = 0.0113.This data shows strong evidence that the proportion of 1500 sq.ft.housing is less than 75%

Question 4

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

Accepted Answer

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.

Question 5

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)  
B)  
C)  
D)  
E)

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.A current survey of 1000 random Canadians found that 245 were obese.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

A)

: p = 0.231;

: p  0.231;z = 1.05;P-value = 0.1469.This data shows virtually no evidence of an increase from the 23.1% of obese Canadians. 
D)

: p = 0.231;

: p > 0.231;z = -1.05;P-value = 0.0594.This data shows virtually no evidence of an increase from the 23.1% of obese Canadians. 
E)

: p = 0.231;

: p > 0.231;z = 1.05;P-value = 0.8531.This data shows virtually no evidence of an increase from the 23.1% of obese Canadians.

Question 7

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.Create a 95% confidence interval for the proportion of participant weight loss.

Accepted Answer

A) Based on the data,we are 95% confident the proportion of participant weight loss is between 64.56% and 79.44%. 
B) Based on the data,we are 95% confident the proportion of participant weight loss is between 64.56% and 85.44%. 
C) Based on the data,we are 95% confident the proportion of participant weight loss is between 57.84% and 98.16%. 
D) Based on the data,we are 95% confident the proportion of participant weight loss is between 72% and 84%. 
E) Based on the data,we are 95% confident the proportion of participant weight loss is between 71.14% and 84.86%.

Question 8

Five years ago,a company found that 8% of its employees commuted to work by car.A test for the current proportion of commuting employees was done on a random sample of 1000 employees,and found car commuting to be 12%.Create a 95% confidence interval for the proportion of employee commute by car.

Accepted Answer

A) Based on the data,we are 95% confident the proportion of employee commute by car is between 8% and 16%. 
B) Based on the data,we are 95% confident the proportion of employee commute by car is between 4.64% and 19.36%. 
C) Based on the data,we are 95% confident the proportion of employee commute by car is between 6.32% and 13.68%. 
D) Based on the data,we are 95% confident the proportion of employee commute by car is between 9.99% and 14.01%. 
E) Based on the data,we are 95% confident the proportion of employee commute by car is between 6.32% and 9.68%.

Question 9

Is the mean weight of female college students equal to 59 kg? To test this,you take a random sample of 80 students,finding a mean of 61 kg with a standard deviation of 8.4 kg.

Accepted Answer

A) Fail to reject the null hypothesis of μ=59 with a P-value of 0.9668.There is not sufficient evidence that the weight of female students has changed. 
B) Fail to reject the null hypothesis of μ=59 with a P-value of 0.0166.There is not sufficient evidence that the weight of female students has changed. 
C) Reject the null hypothesis of μ=59 with a P-value of 0.0332.There is sufficient evidence that the weight of female students has changed. 
D) Reject the null hypothesis of μ=59 with a P-value of 0.0166.There is sufficient evidence that the weight of female students has changed. 
E) There is not enough information to perform the test.

Question 10

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 a current survey of 1000 random Canadians found that 245 were obese.Create a 95% confidence interval for the proportion of Canadians that are currently obese.

Accepted Answer

A) Based on the data,we are 95% confident the current proportion of obese Canadians is between 22% and 24%. 
B) Based on the data,we are 95% confident the current proportion of obese Canadians is between 17.97% and 26.03%. 
C) Based on the data,we are 95% confident the current proportion of obese Canadians is between 17.97% and 27.03%. 
D) Based on the data,we are 95% confident the current proportion of obese Canadians is between 21.8% and 27.2%. 
E) Based on the data,we are 95% confident the current proportion of obese Canadians is between 22.44% and 26.56%.

Question 11

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?

Accepted Answer

A)  
B)  
C)  
D)  
E)

Question 12

Suzie has installed a new spam blocker program on her email.She used to receive an average of 20 spam emails a day.Is the new program working?

Accepted Answer

A)  
B)  
C)  
D)  
E)  Not enough information is given.

Question 13

Has the introduction of more music download services changed the number of university students downloading music online without paying for it? Two years ago,approximately 50,000 college students admitted to downloading music online without paying for it.

Accepted Answer

A)  
B)  
C)  
D)  
E)

Question 14

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.

Accepted Answer

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.

Question 15

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 16

You are considering moving to Richmond Hill and are concerned about the average one-way commute time to downtown Toronto.Does the average one-way commute time exceed 25 minutes? You take a random sample of 100 Richmond Hill residents and find an average commute time of 29 minutes with a standard deviation of 7 minutes.

Accepted Answer

A)  
B)  
C)  
D)  
E)

Question 17

Marc wants to know if the mean age of the employees at his company is less than 26 years.He obtains a random sample of 100 employees,and finds a mean age of 25.1 years and a standard deviation of 9.2 years.

Accepted Answer

A) Fail to reject the null hypothesis of μ = 26 with a P-value of 0.1635.There is not sufficient evidence that the mean age is less than 26 years. 
B) Reject the null hypothesis of μ = 26 with a P-value of 0.0425.The evidence suggests that the mean age is less than 26 years. 
C) Fail to reject the null hypothesis of μ = 26 with a P-value of 0.8365.There is not sufficient evidence that the mean age is less than 26 years. 
D) Reject the null hypothesis of μ = 26 with a P-value of 0.018.There is sufficient evidence that the mean age is less than 26 years. 
E) There is not enough information to perform the test.

Question 18

You want to see if the number of minutes cell phone users use each month has changed from its mean of 120 minutes 2 years ago.You take a random sample of 100 cell phone users and find an average of 135 minutes used.

Accepted Answer

A)  
B)  
C)  
D)  
E)

Question 19

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 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

A) : p = 0.72; : p ≠ 0.72;z = 1.58;P-value = 0.1236.This data shows weak evidence of a weight loss in more than 72% of the participants in the weight loss strategy;the manager should not continue with this strategy. B) : p = 0.72; : p > 0.72;z = 1.58;P-value = 0.0571.This data shows moderate evidence of a weight loss in more than 72% of the participants in the weight loss strategy;it is hard to say whether or not they should use this strategy,perhaps further testing is in order. C) : p = 0.72; : p > 0.72;z = -1.58;P-value = 0.0618.This data shows weak evidence of a weight loss in more than 72% of the participants in the weight loss strategy;the manager should change strategies. D) : p = 0.72; : p < 0.72;z = -1.58;P-value = 0.9382.This data shows conclusive evidence of a weight loss in more than 72% of the participants in the weight loss strategy;the manager should continue with this strategy. E) : p = 0.72; : p < 0.72;z = 1.58;P-value = 0.9382.This data shows conclusive evidence of a weight loss in more than 72% of the participants in the weight loss strategy;the manager should continue with this strategy.

Question 20

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 found the retention rate at 5%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

A)

: p = 0.04;

: p > 0.04;z = 0.96;P-value = 0.1685.This data shows virtually no evidence that more than 4% of students are retained;the university should not continue with the new programs. 
B)

: p = 0.04;

: p  0.04;z = -1.07;P-value = 0.1423.This data does not show that more than 4% of students are retained;the university should not continue with the new programs. 
E)

: p = 0.04;

: p ≠ 0.04;z = 1.07;P-value = 0.2846.This data shows virtually no evidence that more than 4% of students are retained;the university should not continue with the new programs.

Exam 19: Testing Hypotheses About Proportions

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.

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 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 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.Create a 95% confidence interval for the proportion of participant weight loss.

Five years ago,a company found that 8% of its employees commuted to work by car.A test for the current proportion of commuting employees was done on a random sample of 1000 employees,and found car commuting to be 12%.Create a 95% confidence interval for the proportion of employee commute by car.

Is the mean weight of female college students equal to 59 kg? To test this,you take a random sample of 80 students,finding a mean of 61 kg with a standard deviation of 8.4 kg.

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?

Suzie has installed a new spam blocker program on her email.She used to receive an average of 20 spam emails a day.Is the new program working?

Has the introduction of more music download services changed the number of university students downloading music online without paying for it? Two years ago,approximately 50,000 college students admitted to downloading music online without paying for it.

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?

Marc wants to know if the mean age of the employees at his company is less than 26 years.He obtains a random sample of 100 employees,and finds a mean age of 25.1 years and a standard deviation of 9.2 years.

You want to see if the number of minutes cell phone users use each month has changed from its mean of 120 minutes 2 years ago.You take a random sample of 100 cell phone users and find an average of 135 minutes used.