Exam 17: Testing Hypotheses About Proportions

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.What are the null and alternative hypotheses?

A new manager,hired at a large warehouse,was told to reduce the 26% employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager decides to test the new program to see if it's better.What are the null and alternative hypotheses?

Are Canadians getting fatter? Researchers interested in this question take a random sample of 500 people and record an average weight of 86 kg.Ten years ago,the average weight was 83 kg.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Statistics Canada claims that the current unemployment rate is lower than that of April 2011.To test this claim,a hypothesis test is conducted and yields a P-value turns out to be 0.04.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,the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

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 or higher.Suppose you believe that the percentage of obese Canadians has increased since 2004 and wish to test your belief.Based on a 2014 survey,you conduct a hypothesis test and come up with a P-value of 0.028.What is reasonable to conclude?

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?

Suzie has installed a new spam blocker program on her email.She used to receive an average of 20 spam emails a day.Is the new program working?

After a political ad campaign for a city's mayor,pollsters check the disapproval ratings.They test the hypothesis that the ads produced no change against the alternative that the ratings are now below 19%,and find a P-value of 0.17.Provide an appropriate conclusion.

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%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

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 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.

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.

You are considering moving to Richmond Hill and are concerned about the average one-way commute time to downtown Toronto.Does the average one-way commute time exceed 25 minutes? You take a random sample of 100 Richmond Hill residents and find an average commute time of 29 minutes with a standard deviation of 7 minutes.

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?

A weight loss program provided a loss for 60% of its participants.The program leader decides to test a new weight loss strategy to see if it's better and gets a P-value of 0.21.Is it reasonable to conclude that the new strategy and the old one are equally effective?

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?

A new manager,hired at a large warehouse,was told to reduce the 26% employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager decides to test the new program to see if it's better and receives a P-value of 0.06.What is reasonable to conclude about the new strategy?

At a local university,only 62% of the original freshman class graduated in four years.Has this percentage changed?