Exam 8: Inference for Proportions

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 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?

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 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?

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 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 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 ?

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 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 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 manufacturer receives parts from two suppliers.A simple random sample of 400 parts from Supplier 1 finds 20 defective.A simple random sample of 200 parts from Supplier 2 finds 20 defective.Let p₁ and p₂ be the proportion of all parts from Supplier 1 and Supplier 2,respectively,that are defective.What is the relative risk that a part from Supplier 1 is defective as compared to a part from Supplier 2?

At a large Midwestern university,a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen finished in the bottom third of their high school class.Admission standards at the university were tightened in 1995.In 1997,a simple random sample of 100 entering freshmen found that only 10 finished in the bottom third of their high school class.Let p₁ and p₂ be the proportions of all entering freshmen in 1993 and 1997,respectively,who graduated in the bottom third of their high school class.What is a 90% plus four confidence interval for p₁ - p₂?

Are parents of girls more inclined to buy them a car when they leave for college than parents of boys? Simple random samples of 40 girls and 45 boys are taken from a large university on the West Coast.When interviewed,20 girls and 21 boys in the sample responded that their parents bought them a car.What is a 95% plus four confidence interval for the difference in population proportions of girls and boys whose parents bought a car for them when they left for college? Use girls as Group 1 and boys as Group 2.

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 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 manufacturer receives parts from two suppliers.A simple random sample of 400 parts from Supplier 1 finds 20 defective.A simple random sample of 200 parts from Supplier 2 finds 20 defective.Let p₁ and p₂ be the proportion of all parts from Supplier 1 and Supplier 2,respectively,that are defective.Would a 95% confidence interval for p₁ - p₂ contain the value zero?

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 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^*.

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

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