Exam 19: Testing Hypotheses About Proportions

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 reevaluates its retention rate and comes up with a P-value of 0.075.What is reasonable to conclude about the new programs?

Census data for a certain city shows that 22% of residents are European.Suppose 94 people are called for jury duty,and only 15 of them are European.Does this call into question the fairness of the jury selection system? Use a calculator to find z-scores and P-values.

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%.Create a 95% confidence interval for the proportion of housing 1500 sq.ft.

Data in 1980 showed that about 42% of one country's population had never smoked cigarettes.In 2004,a national health survey in this country interviewed a random sample of 3000 adults and found that 51% had never been smokers.Create a 95% confidence interval for the proportion in 2004 of this country's adults who had never been smokers.

4% of trucks of a certain model have needed new engines after being driven between 0 and 100 kilometres.The manufacturer hopes that the redesign of one of the engine's components has solved this problem.

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy to see if it's better.What are the null and alternative hypotheses?

Is the mean lifetime of particular type of car engine greater than 350,000 km? To test this claim,a sample of 100 engines is measured,yielding an average of 354,585 km and a standard deviation of 18515 km.

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.An independent agency ran a test on a random sample size of 10000 and found the chlorine level at 0.5% mg/mL.Create a 95% confidence interval for the proportion of chlorine in the water.

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.What are the null and alternative hypotheses?

A test of sobriety involves measuring the subject's motor skills.Sixty-four randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.4.Test the claim that the true mean score for all sober subjects is equal to 40.5.

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.If we wish to support our claim,what are the null and alternative hypotheses?

Health Canada reports that,in 2005,85% of Canadians were satisfied with the health care services they received.Suppose you are now concerned that a smaller percentage of Canadians are satisfied with the health care services they received.If you want to justify your concerns,what are the null and alternative hypotheses?

A newspaper is considering the launch of an online edition.The newspaper plans to go ahead only if it's convinced that more than 35% of current readers would subscribe.The newspaper contacts a simple random sample of 1000 current subscribers,and 345 of those surveyed expressed interest.What should the company do? Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.Use a calculator to find z-scores and P-values.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.Suppose a test was conducted on current unemployment and a random sample size of 1000 and found unemployment at 3.8%.Create a 95% confidence interval for the proportion of unemployment.

A company hopes to improve its engines,setting a goal of no more than 3% of customers using their warranty on defective engine parts.A random survey of 1200 customers found only 20 with complaints.Create a 95% confidence interval for the true level of warranty users among all customers.

During the 2004 season,home teams in the same conference won 189 out of 302 regular season college basketball games.Test the home team advantage hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

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.The P-value turns out to be 0.025.Provide an appropriate conclusion.

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,in 2004 the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%.Create a 95% confidence interval for the proportion of students (in 2004)who had been retained.

A mayor is concerned about the percentage of city residents who express disapproval of his job performance.His political committee pays for a newspaper ad,hoping that it will keep the disapproval rate below 21%.They will use a follow-up poll to assess the ad's effectiveness.

A survey investigation whether the proportion of employees who commute by car to work is higher than it was five years ago finds a P-value of 0.009.Is it reasonable to conclude that more employees are commuting by car?