Deck 8: Inference for Proportions

Question 1

The candy company that makes M&M's claims that 10% of the M&M's it produces is green.Suppose that the candies are packaged at random in large bags of 200 M&M's.When we randomly pick a bag of M&M's,we may assume that this represents a simple random sample of size n = 200.Suppose we wish to test H₀: p = 0.10 versus H_a: p  0.10.Under the null hypothesis,what is the value of the standard error of ,the sample proportion of green M&M's in a bag of 200?

A)0.0015
B)0.021
C)0.09
D)18

Answer 1

0.021

Question 2

The Information Technology Department at a large university wishes to estimate the proportion of students living in the dormitories,p,who own a computer with a 95% confidence interval.What is the minimum required sample size the IT Department should use to estimate the proportion p with a margin of error no larger than 3 percentage points?

A)33
B)752
C)1067
D)1068

Answer 2

1068

Question 3

A simple random sample of 100 athletes is selected from a large high school.In the sample,there are 15 football players.What is the standard error of the sample proportion of football players?

A)0.00128
B)0.0357
C)0.05
D)0.357

Answer 3

0.0357

Question 4

A simple random sample of 450 residents in the state of New York is taken to estimate the proportion of people who live within 1 mile of a hazardous waste site.If 315 of the residents in the sample live within 1 mile of a hazardous waste site,what are the values of the sample proportion of people who live within 1 mile of a hazardous waste site and its standard error?

A)0.3 and 0.022
B)0.7 and 0.01
C)0.7 and 0.21
D)0.7 and 0.022

Question 5

The candy company that makes M&M's claims that 10% of the M&M's it produces are green.Suppose that the candies are packaged at random,and the small bags contain 25 M&M's.When we randomly pick a bag of M&M's,we may assume that this represents a simple random sample of size n = 25.Suppose that in a randomly selected small bag of M&M's,there are 5 green M&M's.What is a 99% plus four confidence interval for p,the population proportion of green M&M's?

A)(0,0.4061)
B)(0.0161,0.4283)
C)(0.0367,0.4461)
D)(0.0856,0.3971)

Question 6

A simple random sample of 100 bags of tortilla chips produced by Company X is selected every hour for quality control.In the current sample,18 bags had more chips (measured in weight)than the labeled quantity.The quality control inspector wishes to use this information to calculate a 90% confidence interval for the true proportion of bags of tortilla chips that contain more than the label states.What is the value of the standard error of ?

A)0.0015
B)0.038
C)0.063
D)0.384

Question 7

A simple random sample of 450 residents in the state of New York is taken to estimate the proportion of people who live within 1 mile of a hazardous waste site.If a 95% confidence interval were calculated for a scenario where p = 0.3 and another scenario where p = 0.7,how would the two confidence intervals compare?

A)Since the sample proportion in the first scenario is smaller,its confidence interval would be narrower.
B)Even though the sample proportions are different,the widths of the confidence intervals would be equal.
C)Since the sample proportion in the second scenario is larger,its confidence interval would be shifted to the right and narrower than the one calculated from the first scenario.
D)This cannot be determined from the information given.

Question 8

A noted psychic was tested for extrasensory perception.The psychic was presented with 200 cards face down and asked to determine if each card were one of five symbols: a star,a cross,a circle,a square,or three wavy lines.The psychic was correct in 50 cases.Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial.Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime.Based on the results of the test,what is a 95% confidence interval for p?

A)0.25 ± 0.004
B)0.25 ± 0.05
C)0.25 ± 0.055
D)0.25 ± 0.060

Question 9

A simple random sample of 120 vet clinics in the Midwest reveals that the vast majority of clinics only treat small pets (dogs,cats,rabbits,etc. )and not large animals (cows,horses,etc. ).Of the 120 clinics sampled,88 responded that they do not treat large animals at their clinic.What is the value of the standard error of ?

A)0.02
B)0.03
C)0.04
D)0.05

Question 10

A simple random sample of 120 vet clinics in the Midwest reveals that the vast majority of clinics only treat small pets (dogs,cats,rabbits,etc. )and not large animals (cows,horses,etc. ).Of the 120 clinics sampled,88 responded that they do not treat large animals at their clinic.If a 95% confidence interval were calculated instead of 90% confidence interval,what would happen to the width of the confidence interval?

A)It would be narrower.
B)It would stay the same.
C)It would be wider.
D)This cannot be determined from the information given.

Question 11

The candy company that makes M&M's claims that 10% of the M&M's it produces are green.Suppose that the candies are packaged at random,and the small bags contain 25 M&M's.When we randomly pick a bag of M&M's,we may assume that this represents a simple random sample of size n = 25.Suppose that in a randomly selected small bag of M&M's,there are 5 green M&M's.At the 1% significance level,are the data statistically significant for testing if the true proportion of green M&M's is indeed equal to 10%?

A)Yes
B)No
C)This cannot be determined from the information given.

Question 12

The candy company that makes M&M's claims that 10% of the M&M's it produces is green.Suppose that the candies are packaged at random in large bags of 200 M&M's.When we randomly pick a bag of M&M's,we may assume that this represents a simple random sample of size n = 200.Suppose we wish to test H₀: p = 0.10 versus H_a: p  0.10.Suppose that in the randomly selected bag of M&M's there are only 12 green M&M's.What is the value of the large-sample z statistic?

A)z = -1.886
B)z = -0.444
C)z = 1.886
D)z = 0.444

Question 13

The candy company that makes M&M's claims that 10% of the M&M's it produces are green.Suppose that the candies are packaged at random,and the small bags contain 25 M&M's.When we randomly pick a bag of M&M's,we may assume that this represents a simple random sample of size n = 25.Suppose that in a randomly selected small bag of M&M's,there are 5 green M&M's.What is the value of the standard error of ?

A)0.0063
B)0.0794
C)0.08
D)0.10

Question 14

The candy company that makes M&M's claims that 10% of the M&M's it produces is green.Suppose that the candies are packaged at random in large bags of 200 M&M's.When we randomly pick a bag of M&M's,we may assume that this represents a simple random sample of size n = 200.Suppose we wish to test H₀: p = 0.10 versus H_a: p  0.10.Suppose that in the randomly selected bag of M&M's there are only 12 green M&M's.Calculate the value of the large-sample z statistic.What is the value of the corresponding P-value?

A)P-value = 0.0297
B)P-value = 0.0593
C)P-value = 0.06
D)P-value = 0.3284

Question 15

The candy company that makes M&M's claims that 10% of the M&M's it produces are green.Suppose that the candies are packaged at random,and the small bags contain 25 M&M's.When we randomly pick a bag of M&M's,we may assume that this represents a simple random sample of size n = 25.Suppose that in a randomly selected small bag of M&M's,there are 5 green M&M's.What is the plus four estimate of the proportion of green M&M's?

A) = 0.1724
B) = 0.2
C) = 0.222
D) = 0.2414

Question 16

A simple random sample of 85 students is taken from a large university on the West Coast to estimate the proportion of students whose parents bought a car for them when they left for college.When interviewed,51 students in the sample responded that their parents bought them a car.What is a 95% confidence interval for p,the population proportion of students whose parents bought a car for them when they left for college?

A)(0.296,0.504)
B)(0.463,0.737)
C)(0.496,0.704)
D)(0.513,0.687)

Question 17

A simple random sample of 450 residents in the state of New York is taken to estimate the proportion of people who live within 1 mile of a hazardous waste site.If 135 of the residents in the sample live within 1 mile of a hazardous waste site,what are the values of the sample proportion of people who live within 1 mile of a hazardous waste site and its standard error?

A)0.3 and 0.01
B)0.3 and 0.022
C)0.3 and 0.21
D)0.7 and 0.022

Question 18

A simple random sample of 120 vet clinics in the Midwest reveals that the vast majority of clinics only treat small pets (dogs,cats,rabbits,etc. )and not large animals (cows,horses,etc. ).Of the 120 clinics sampled,88 responded that they do not treat large animals at their clinic.What is a 90% confidence interval for p,the population proportion of vet clinics that do treat large animals?

A)(0.163,0.371)
B)(0.188,0.346)
C)(0.200,0.333)
D)(0.667,0.800)

Question 19

The candy company that makes M&M's claims that 10% of the M&M's it produces is green.Suppose that the candies are packaged at random in large bags of 200 M&M's.When we randomly pick a bag of M&M's,we may assume that this represents a simple random sample of size n = 200.Suppose we wish to test H₀: p = 0.10 versus H_a: p  0.10.Suppose that in the randomly selected bag of M&M's there are only 12 green M&M's.Calculate the value of the large-sample z statistic.If a 90% confidence interval were also calculated from the data,would it contain the value 0.10?

A)Yes
B)No
C)This cannot be determined from the information given.

Question 20

A simple random sample of 60 blood donors is taken to estimate the proportion of donors with type A blood with a 95% confidence interval.In the sample,there are 10 people with type A blood.What is the margin of error for this confidence interval?

A)0.048
B)0.079
C)0.094
D)1.96

Question 21

An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips.If there is clear evidence that this proportion is less than 0.10,she will accept the shipment.To reach a decision,she will test the hypotheses H₀: p = 0.10 versus H_a: p < 0.10.To do so,she selects a simple random sample of 150 potatoes from the more than 3000 potatoes on the truck.Only 8 of the potatoes sampled are found to have major defects.Compute the value of the large-sample z statistic and the P-value for this hypothesis test.At which of the following significance levels are the data statistically significant? There can be more than one correct answer.

A) = 0.01
B) = 0.025
C) = 0.05
D) = 0.10

Question 22

A noted psychic was tested for extrasensory perception.The psychic was presented with 200 cards face down and asked to determine if each card were one of five symbols: a star,a cross,a circle,a square,or three wavy lines.The psychic was correct in 50 cases.Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial.Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime.What do we know about the value of the P-value for the hypothesis test? (Note: Use the large-sample z statistic. )

A)P-value < 0.001
B)0.001 < P-value < 0.01
C)0.01 < P-value < 0.05
D)0.05 < P-value < 0.10

Question 23

A quality manager in a small manufacturing company wants to estimate the proportion of items produced by a very specialized process that fail to meet a customer's specification.Because it is very expensive to determine if an item produced by the process meets the specification,only a very small number of items can be tested.A random sample of 15 items was selected,and in the sample three of them failed.Based on the sample results,the plus four estimate of the true proportion of items that failed to meet the customer's specifications is _______.

A) = 0.200
B) = 0.158
C) = 0.333
D) = 0.263
E)Not within ± 0.02 of any of the above

Question 24

A noted psychic was tested for extrasensory perception.The psychic was presented with 200 cards face down and asked to determine if each card were one of five symbols: a star,a cross,a circle,a square,or three wavy lines.The psychic was correct in 50 cases.Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial.Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime.Suppose you wished to see if there was evidence that the psychic is doing better than just guessing.To do this,you test the hypotheses H₀: p = 0.20 versus H_a: p > 0.20.What is the value of the large-sample z statistic?

A)z = 0.83
B)z = 1.77
C)z = 1.96
D)z = 4.17

Question 25

A study was conducted at the University of Waterloo on the impact characteristics of football helmets used in competitive high school programs.There were three types of helmets considered,classified according to liner type: suspension,padded-suspension,and padded.In the study,a measurement called the Gadd Severity Index (GSI)was obtained on each helmet,using a standardized impact test.A helmet was deemed to have failed if the GSI was greater than 1200.Of the 81 helmets tested,29 failed the GSI 1200 criterion.How many suspension-type helmets should be tested so that the margin of error does not exceed 0.05 with 95% confidence?

A)385
B)20
C)271
D)250
E)82

Question 26

After a college football team once again lost a game to their archrival,the alumni association conducted a survey to see if alumni were in favor of firing the coach.A simple random sample of 100 alumni from the population of all living alumni was taken.Sixty-four of the alumni in the sample were in favor of firing the coach.Let p represent the proportion of all living alumni who favored firing the coach.Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach.To do this they test the hypotheses H₀: p = 0.50 versus H_a: p > 0.50.What is the P-value for this hypothesis test?

A)Below 0.001
B)0.0026
C)0.0682
D)0.14

Question 27

An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips.If there is clear evidence that this proportion is less than 0.10,she will accept the shipment.To reach a decision,she will test the hypotheses H₀: p = 0.10 versus H_a: p < 0.10.To do so,she selects a simple random sample of 150 potatoes from the more than 3000 potatoes on the truck.Only 8 of the potatoes sampled are found to have major defects.Compute the value of the large-sample z statistic.What is the P-value for this hypothesis test?

A)Less than 0.0002
B)0.0098
C)0.0284
D)0.0568

Question 28

A noted psychic was tested for extrasensory perception.The psychic was presented with 200 cards face down and asked to determine if each card were one of five symbols: a star,a cross,a circle,a square,or three wavy lines.The psychic was correct in 50 cases.Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial.Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime.How large a sample n would you need to estimate p with a margin of error of 0.01 with 95% confidence? Use the hypothesized value p = 0.20 as the value for p^*.

A)n = 32
B)n = 1537
C)n = 6147
D)n = 9604

Question 29

An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips.If there is clear evidence that this proportion is less than 0.10,she will accept the shipment.To reach a decision,she will test the hypotheses H₀: p = 0.10 versus H_a: p < 0.10.To do so,she selects a simple random sample of 150 potatoes from the more than 3000 potatoes on the truck.Only 8 of the potatoes sampled are found to have major defects.What is the value of the large-sample z statistic?

A)z = -2.33
B)z = -1.91
C)z = 2.33
D)z = 1.91

Question 30

A quality manager in a small manufacturing company wants to estimate the proportion of items produced by a very specialized process that fail to meet a customer's specification.Because it is very expensive to determine if an item produced by the process meets the specification,only a very small number of items can be tested.A random sample of 15 items was selected,and in the sample three of them failed.At the 98% confidence level,what is the margin of error in the plus four estimate of p?

A)0.198
B)0.023
C)0.235
D)0.261
E)Not within ± 0.01 of any of the above

Question 31

A quality manager in a small manufacturing company wants to estimate the proportion of items produced by a very specialized process that fail to meet a customer's specification.Because it is very expensive to determine if an item produced by the process meets the specification,only a very small number of items can be tested.A random sample of 15 items was selected,and in the sample three of them failed.What is the standard error of the plus four estimate of the true proportion p?

A)0.010
B)0.103
C)0.101
D)0.116
E)0.013

Question 32

After a college football team once again lost a game to their archrival,the alumni association conducted a survey to see if alumni were in favor of firing the coach.A simple random sample of 100 alumni from the population of all living alumni was taken.Sixty-four of the alumni in the sample were in favor of firing the coach.Let p represent the proportion of all living alumni who favored firing the coach.What is a 99% confidence interval for p?

A)0.64 ± 0.048
B)0.64 ± 0.079
C)0.64 ± 0.094
D)0.64 ± 0.124

Question 33

After a college football team once again lost a game to their archrival,the alumni association conducted a survey to see if alumni were in favor of firing the coach.A simple random sample of 100 alumni from the population of all living alumni was taken.Sixty-four of the alumni in the sample were in favor of firing the coach.Let p represent the proportion of all living alumni who favored firing the coach.Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach.To do this they test the hypotheses H₀: p = 0.50 versus H_a: p > 0.50.The alumni association wished to conduct the test at a 5% significance level.What would their decision be? Based on that decision,what type of mistake could they have made?

A)Do not reject H₀;Type I error
B)Do not reject H₀;Type II error
C)Reject H₀;Type I error
D)Reject H₀;Type II error

Question 34

A newspaper is conducting a statewide survey concerning the race for governor.The newspaper will take a simple random sample of n registered voters and determine X = the number of voters that will vote for the Democratic candidate.Is there evidence that a clear majority of the population will vote for the Democratic candidate? To answer this,they will test the hypotheses H₀: p = 0.50 versus H_a: p > 0.50.Consider the two scenarios,where in Scenario 1,n = 1200 and X = 640.In Scenario 2,n = 120 and X = 64.Even though the values for are the same in the two scenarios,we come to opposite decisions (we reject H₀ in one scenario and we do not in the other).What is the reason for these contrasting decisions?

A)When the sample size is larger,the margin of error is larger.This may cause the results to be biased.
B)The 64 people in the small sample must also be part of the 640 people in the big sample.This means we are counting them twice,causing the results of the test with the larger sample to be wrong.
C)The sample size in the first scenario is much larger,leading to a test with higher power.
D)We must have made a mistake.With equal values of ,we must come to equal decisions.

Question 35

A supplier of television programs through a satellite service is planning to offer a new package and would like to determine what proportion of the households in their region would purchase this new package.Based on past experience it is thought that it is likely 25% to 35% of households will purchase the package.If the supplier wants to be 95% confident in the outcome,how many households should they randomly sample to achieve a margin of error no greater than ± 0.025 in their estimate?

A)922
B)985
C)350
D)1399
E)Not within ± 25 of any of the above

Question 36

A newspaper is conducting a statewide survey concerning the race for governor.The newspaper will take a simple random sample of n registered voters and determine X = the number of voters that will vote for the Democratic candidate.Is there evidence that a clear majority of the population will vote for the Democratic candidate? To answer this,they will test the hypotheses H₀: p = 0.50 versus H_a: p > 0.50.If n = 1200 and X = 640,what is the P-value for this hypothesis test?

A)Less than 0.0002
B)0.0105
C)0.0330
D)0.2326

Question 37

A study was conducted at the University of Waterloo on the impact characteristics of football helmets used in competitive high school programs.There were three types of helmets considered,classified according to liner type: suspension,padded-suspension,and padded.In the study,a measurement called the Gadd Severity Index (GSI)was obtained on each helmet,using a standardized impact test.A helmet was deemed to have failed if the GSI was greater than 1200.Of the 81 helmets tested,29 failed the GSI 1200 criterion.Assume that the suspension helmets tested were selected at random.What are the point estimates of the proportion of suspension helmets that fail and the standard error of the estimate,respectively?

A)0.36;0.0028
B)0.64;0.053
C)0.36;0.053
D)0.64;0.0028
E)0.36;0.089

Question 38

A study was conducted at the University of Waterloo on the impact characteristics of football helmets used in competitive high school programs.There were three types of helmets considered,classified according to liner type: suspension,padded-suspension,and padded.In the study,a measurement called the Gadd Severity Index (GSI)was obtained on each helmet,using a standardized impact test.A helmet was deemed to have failed if the GSI was greater than 1200.Of the 81 helmets tested,29 failed the GSI 1200 criterion.Based on the sample results,what is the 90% confidence interval estimate for the true population proportion of suspension helmets that would fail the test?

A)(0.304,0.416)
B)(0.256,0.464)
C)(0.213,0.507)
D)(0.272,0.448)
E)(0.553,0.737)

Question 39

A recent study used umbilical cord blood to test for 25 hydroxyvitamin D,which is an indicator of vitamin D status of the baby.It was reported that 65% of babies tested were deficient in vitamin D in spite of the fact that the mothers consumed vitamin D supplements during pregnancy.A researcher in a northern region felt that this percentage was too high for this region because with the reduced hours of sunshine during winter months,pregnant women tended to use higher doses of supplements to compensate.A sample of 125 newborns was tested,and 72 were declared to be deficient in vitamin D.What would be the appropriate null and alternative hypotheses that the researcher should establish for a test of significance?

A)H₀: p = 0.5;H_a: p < 0.5
B)H₀: p = 0.65;H_a: p  0.65
C)H₀: = 0.65;H_a:
< 0.65
D)H₀: p = 0.65;H_a: p < 0.65
E)H₀: = 0.65;H_a:
 0.65

Question 40

A newspaper is conducting a statewide survey concerning the race for governor.The newspaper will take a simple random sample of n registered voters and determine X = the number of voters that will vote for the Democratic candidate.Is there evidence that a clear majority of the population will vote for the Democratic candidate? To answer this,they will test the hypotheses H₀: p = 0.50 versus H_a: p > 0.50.If n = 120 and X = 64,what is the P-value for this hypothesis test?

A)Less than 0.0002
B)0.0104
C)0.0330
D)0.2326

Question 41

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.What is the count X of SSIs in this study?

A)780,000
B)277
C)278
D)1

Question 42

A simple random sample of 200 students is selected from a large university.In this sample,there are 35 minority students.A simple random sample of 80 students is selected from the community college in the same town.In this sample,there are 28 minority students.What is the standard error of the difference in sample proportions of minority students?

A)0.004
B)0.03
C)0.06
D)0.08

Question 43

When calculating a sample size for a certain margin of error m,what value of p^* will result in the largest sample size?

A).5
B).05
C)0
D)1

Question 44

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.What is the approximate distribution of
?

A)Normal
B)Uniform
C)T
D)F

Question 45

A recent study used umbilical cord blood to test for 25 hydroxyvitamin D,which is an indicator of vitamin D status of the baby.It was reported that 65% of babies tested were deficient in vitamin D in spite of the fact that the mothers consumed vitamin D supplements during pregnancy.A researcher in a northern region felt that this percentage was too high for this region because with the reduced hours of sunshine during winter months,pregnant women tended to use higher doses of supplements to compensate.A sample of 125 newborns was tested,and 72 were declared to be deficient in vitamin D.What is the P-value and the conclusion using  = 0.05?

A)P = 0.042;do not reject H₀ since the P-value is less than the given  level.
B)P = 0.047;do not reject H₀ because it is significant at the given  level.
C)P = 0.084;the result is not significant at the  = 0.05 level.
D)P = 0.041;reject H₀ since the P-value is less than the given  level.
E)We are unable to calculate the P-value or reach a conclusion with the information given.

Question 46

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.What is the standard error of
?

A)0
B)Around .004
C)Greater than .1
D)None of the above

Question 47

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.What is the mean of the distribution of
?

A).019
B).004
C)780,000
D)None of the above

Question 48

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.What test statistic is used to test the hypothesis that the Georgetown medical office SSIs rate is less than the national average SSIs rate?

A)-1.876
B)1.876
C).03
D)None of the above

Question 49

A sociologist is studying the effect of having children within the first 2 years of marriage on the divorce rate.Using hospital birth records,she selects a simple random sample of 200 couples who had children within the first 2 years of marriage.Following up on these couples,she finds that 80 couples are divorced within 5 years.Let p = the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years.What is a 90% plus four confidence interval for the proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years?

A)0.402 ± 0.035
B)0.402 ± 0.057
C)0.402 ± 0.067
D)0.402 ± 0.088

Question 50

A sociologist is studying the effect of having children within the first 2 years of marriage on the divorce rate.Using hospital birth records,she selects a simple random sample of 200 couples who had children within the first 2 years of marriage.Following up on these couples,she finds that 80 couples are divorced within 5 years.Let p = the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years.Is the sample size of n = 200 large enough to estimate p with a margin of error 0.05 with 90% confidence? Use the observed value 0.40 as the value for p^*.

A)Yes
B)No
C)This cannot be determined from the information given.

Question 51

A sociologist is studying the effect of having children within the first 2 years of marriage on the divorce rate.Using hospital birth records,she selects a simple random sample of 200 couples who had children within the first 2 years of marriage.Following up on these couples,she finds that 80 couples are divorced within 5 years.Let p = the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years.Suppose the sociologist wishes to test H₀: p = ⅓ versus H_a: p  ⅓.At the 10% significance level,are the data statistically significant for testing these hypotheses?

A)Yes
B)No
C)This cannot be determined from the information given.

Question 52

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.What is an 80% confidence interval for
?

A)(.004,.011)
B)(0,1)
C)(-.001,.008)
D)None of the above

Question 53

The level C confidence interval for a proportion p will have a margin of error approximately equal to a specified value m when the sample size satisfies .What does the p^* represent?

A)A guessed value of p
B)A guessed value of

C)The true value of

D)The true value of p

Question 54

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.Is the Georgetown medical office SSIs rate less than the national average SSIs rate? (Note: Use a significance level of .05. )

A)Yes,because the P-value is less than .05
B)Yes,because the P-value is greater than .05
C)No,because the P-value is less than .05
D)No,because the P-value is greater than .05

Question 55

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.What is the sample size n in this study?

A)780,000
B)277
C)278
D)1

Question 56

A recent study used umbilical cord blood to test for 25 hydroxyvitamin D,which is an indicator of vitamin D status of the baby.It was reported that 65% of babies tested were deficient in vitamin D in spite of the fact that the mothers consumed vitamin D supplements during pregnancy.A researcher in a northern region felt that this percentage was too high for this region because with the reduced hours of sunshine during winter months,pregnant women tended to use higher doses of supplements to compensate.A sample of 125 newborns was tested,and 72 were declared to be deficient in vitamin D.Based on the data from this region,what is the value of the appropriate test statistic?

A)-1.73
B)-1.32
C)-1.96
D)-1.68
E)-2.01

Question 57

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.What is a 95% confidence interval for
?

A)(.004,.011)
B)(0.1)
C)(-.001,.008)
D)None of the above

Question 58

The margin of error includes the effects of sampling variability,nonresponse bias,and all other sources of errors possible in a study.

Question 59

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.Is the Georgetown medical office SSIs rate less than the national average SSIs rate? (Note: Use a significance level of .01)

A)Yes,because the P-value is less than .01
B)Yes,because the P-value is greater than .01
C)No,because the P-value is less than .01
D)No,because the P-value is greater than .01

Question 60

It is estimated that 780,000 surgical site infections (SSIs)occur each year.SSIs are the second most common type of healthcare-associated infections in U.S.hospitals and account for an extra $3.5 to $10 billion in healthcare costs per year.The national SSIs rate is 1.9%.A Georgetown medical office was interested in determining if their SSI rate were smaller than the national average.Out of a sample of 277 patients in their study,only one infection occurred.What is the sample proportion ?

A)1/780,000
B)1/277
C)277/780,000
D)None of the above

Question 61

Suppose you are conducting a study to determine if women are better drivers than men.You send your survey to over 1000 students on your campus and 5 students respond that women are better drivers and 4 students respond that women are not better drivers.What is the sample proportion
for women as the better drivers using the large-sample method?

A)5/9
B)5/1000
C)9/1000
D)None of the above

Question 62

Suppose relative risk between and is 1.5.What are appropriate values for and ?

A) = 15 and = 10
B) = 5 and = 10
C) = 10 and = 15
D)None of the above

Question 63

Suppose that =.5, = .2,n₁ = 20,and n₂ = 30.What is the pooled estimate of p₁ and p₂?

A)11/50
B).7
C).7/50
D)None of the above

Question 64

Suppose = .5 and the relative risk between and is 1.What is ?

A)0
B)1
C).5
D)This cannot be determined from the given information.

Question 65

Suppose you are conducting a study to determine if women are better drivers than men.You send your survey to over 1000 students on your campus and 5 students respond that women are better drivers and 4 students respond that women are not better drivers.Which of the methods below should you use to build a confidence interval?

A)Large-sample method
B)Plus four method
C)Multi-sample method
D)Two-sample method

Question 66

A 99% confidence interval is wider than an 80% confidence interval.

Question 67

Suppose that =.5, = .2,n₁ = 20,and n₂ = 30.What is the number of successes,X₂,based on p₂?

A).2
B)6
C)30
D)None of the above

Question 68

Suppose you are conducting a study to determine if women are better drivers than men.You send your survey to over 1000 students on your campus and 5 students respond that women are better drivers and 4 students respond that women are not better drivers. What is the standard error of using the plus four method for women who are better drivers than men?

A)
B)
C)
D)

Question 69

Suppose that =.5, = .2,n₁ = 20,and n₂ = 30.What is the P-value for the hypothesis H₀: p₁ = p₂ versus H_a: p₁  p₂?

A)2.28
B).026
C).3
D)None of the above

Question 70

Suppose you are conducting a study to determine if women are better drivers than men.You send your survey to over 1000 students on your campus and 5 students respond that women are better drivers and 4 students respond that women are not better drivers. The small sample size will result in a ______ confidence interval.

A)narrow
B)wide

Question 71

Suppose that =.5, = .2,n₁ = 20,and n₂ = 30.What is the test statistic to test the hypothesis H₀: p₁ = p₂?

A)2.228
B).026
C).3
D)None of the above

Question 72

Suppose that =.5, = .2,n₁ = 20,and n₂ = 30.What is the pooled standard error?

A).12
B).01
C)0
D)None of the above

Question 73

An approximate 99% confidence interval for an unknown proportion p is of the form

± the margin of error.

Question 74

The test statistic for comparing two proportions is based on the ______ distribution.

A)Normal
B)binomial
C)T
D)F

Question 75

Suppose that =.5, = .2,n₁ = 20,and n₂ = 30.What is the mean of the sampling distribution p₁ - p₂?

A).3
B).018
C)0
D)None of the above

Question 76

Suppose that =.5, = .2,n₁ = 20,and n₂ = 30.What is the number of successes,X₁,based on p₁?

A)0
B).5
C)10
D)20

Question 77

Suppose that =.5, = .2,n₁ = 20,and n₂ = 30.What is the standard deviation of the sampling distribution p₁ - p₂?

A).0125
B).005
C).0178
D)None of the above

Question 78

The large-sample significance test for population proportion is based on a z statistic.

Question 79

Suppose = .3 and = .5.What is the relative risk?

A)1.67
B)1
C)0
D).6

Question 80

Suppose you are conducting a study to determine if women are better drivers than men.You send your survey to over 1000 students on your campus and 5 students respond that women are better drivers and 4 students respond that women are not better drivers. What is the sample proportion

for women as the better drivers using the plus four method?

A)5/9
B)7/13
C)9/13
D)None of the above