Exam 9: Hypothesis Testing

Consider the following competing hypotheses: H_o:μ = 0,H_A:μ ≠ 0.The value of the test statistic is z = −1.38.If we choose a 5% significance level,then we ___________________________________________.

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60.The population standard deviation is assumed to equal 0.40.At a 5% significance level,the decision is to _____________.

If the null hypothesis is rejected at a 1% significance level,then _____________.

A city is considering widening a busy intersection in town.Last year,the city reported 16,000 cars passed through the intersection per day.The city conducted a survey for 49 days this year and found an average of 17,000 cars passed through the intersection,with a standard deviation of 5,000. a.Specify the null and alternative hypotheses to determine whether the intersection has seen an increase in traffic. b.Calculate the value of the test statistic and approximate the p-value. c.The city is going to widen the intersection if it believes traffic has increased.At the 5% significance level,can you conclude that the intersection has seen an increase in traffic? Should the city widen the intersection?

A company that manufactures helmets wants to test their helmets to make sure they pass SNELL certification.One of the tests the helmets are required to undergo is a test that simulates real-world impacts.During the test,crash dummies must,on average,experience a force of nearly 300 g in order to pass.The company tests 36 helmets and finds the dummy experienced an average of 298 g with a standard deviation of 8 g. a.Specify the null and alternative hypotheses to determine whether the company's helmets experience,on average,less than 300 g during the SNELL test. b.Calculate the value of the test statistic,and find the critical value at a 10% significance level. c.At the 10% significance level,can you conclude that the company's helmets experience less than 300 g during the SNELL test? Explain.

Which of the following answers represents the objective of a hypothesis test?

A manager at a temp agency believes that one of the agency's recruiters has unorthodox methods and claims that the wages the recruiter secures for its temps differ from the agency's average wage of $12 per hour.The agency takes a random sample of 49 recent contracts the recruiter secured and finds an average wage of $11.25 per hour and a standard deviation of $2.25 per hour.Does the evidence support the agency's claim at the 5% significance level?

A recent report claimed that Americans are retiring later in life (U.S.News & World Report,August 17,2011).An economist wishes to determine if the mean retirement age has increased from 62.To conduct the relevant test,she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t₃₇ = 1.92.With α = 0.05,she ____________________________________________________.

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60.The population standard deviation is assumed to equal 0.40.To establish whether the mean GPA exceeds 3.50,the appropriate hypotheses are ______________.

Excel's function _______ returns the p-value for a right-tailed test.

When conducting a hypothesis test for a given sample size,if the probability of a Type I error decreases,then the ______________________________________.

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose,on average,more than 10 pounds.A consumer activist decides to test the authenticity of the claim.She follows the progress of 18 women who recently joined the weight-reduction program.She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds.Which of the following is an appropriate hypotheses to test the advertisement's claim?

If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05,then the correct conclusion is to ________________.

A(n)______ error is committed when we reject the null hypothesis when the null hypothesis is true.

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later,School Buses Still Late," Boston Globe,October 5,2011).Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route.Historically,the bus service on the route has been,on average,12 minutes late.After the schedule adjustment,the first 36 runs were an average of eight minutes late.As a result,the Boston public school district claimed that the schedule adjustment was an improvement-students were not as late.Assume a population standard deviation for bus arrival time of 12 minutes.At the 1% significance level,does the evidence support the Boston public schools' claim?

The hypothesis statement H: < 60 is an example of a(an)________ hypothesis.

An engineer is designing an experiment to test if airplane engines are faulty and unsafe to fly.The engineer expects 0.0001% of engines to be unsafe.The null hypothesis is that the probability of an unsafe engine is less than or equal to 0.0001% and the alternative hypothesis is that the probability the engine is unsafe is greater than 0.0001%. a.Describe the consequences of Type I and Type II errors. b.Should the engineer design the test with a higher alpha or a higher beta? Explain.

Construct the null and alternative hypotheses for the following claims. a."The school's mean GPA differs from 2.50 GPA." b."The school's mean GPA is less than 2.50 GPA."

Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States,with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune,February 26,2011).But Keurig's patent on K-cups,the plastic pods used to brew the coffee,is expected to expire in 2012,allowing other companies to better compete.Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters.After tweaking its recipe,the competitor conducts a test with 144 tasters,of which 72 prefer its blend.The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast.What critical value should be used to test this claim at the 1% significance level?

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night.If this is to happen,it will have to move one of its most viewed shows to another slot.The network conducts a survey asking its viewers which show they would rather watch.The network receives 827 responses,of which 428 indicate they would like to see the new show in the lineup.Which of the following is an appropriate hypotheses to test if the television network should give its newest show a spot during prime time at night?