Exam 8: Inference for Proportions

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 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 estimate for the difference in proportions,p₁ - p₂?

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

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?

Suppose we have two binomial populations where the true proportion of success is .2 for the first population and .3 for the second population.We take an SRS of size 4 from the first population,and the number of successes is 3.We take an SRS of size 400 from the second population,and the number of successes is 200.What is the standard deviation of - .1?

A simple random sample of 60 households in City 1 is taken.In the sample,there are 45 households that decorate their houses with lights for the holidays.A simple random sample of 50 households is also taken from the neighboring City 2.In the sample,there are 40 households that decorate their houses.We wish to estimate the difference in proportions of households that decorate their houses with lights for the holidays,with a 95% confidence interval.What is the standard error of the difference in sample proportions?

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 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?

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?

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?

If two sample counts of success are equal,then the sample proportions must be equal.

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

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?

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 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 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 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 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?

Suppose the relative risk between and is 1.What are appropriate values for and ?

Suppose we have two binomial populations where the true proportion of success is .2 for the first population and .3 for the second population.We take an SRS of size 4 from the first population,and the number of successes is 3.We take an SRS of size 400 from the second population,and the number of successes is 200.Why should be closer to .3?