Exam 8: Inference for Proportions

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 simple random sample of 100 bags of tortilla chips produced at Plant A is selected every hour for quality control.In the current sample,18 bags had more chips (measured in weight)than the labeled quantity.This sample information is being compared to data collected at Plant B.In the current sample of 100 bags of chips from Plant B,12 bags had more chips than the labeled quantity.Let represent the plus four estimate of the difference in the two proportions.What is the value of the standard error of ?

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?

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

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

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 a 95% confidence interval for the difference in population proportions of households that decorate their houses with lights for the holidays?

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

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 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?

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.

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?

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?

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

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?

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?

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 a possible reason that is not close to .3?

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?

An approximate 99% confidence interval for an unknown proportion p is of the form ± the margin of error.

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?

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