Exam 9: Hypothesis Testing

A portfolio manager claims that the mean annual return on one of the mutual funds he manages exceeds 8%.To substantiate his claim,he states that over the past 10 years,the mean annual return for the mutual fund has been 9.5% with a sample standard deviation of 1.5%.Assume annual returns are normally distributed. a.Specify the competing hypotheses to test the portfolio manager's claim. b.Calculate the value of the test statistic. c.At the 5% significance level,use the critical value approach to state the decision rule. d.Is the portfolio manager's claim substantiated by the data? Explain.

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock.A politician claims that the proportion of babies born out of wedlock is increasing.Identify the correct null and alternative hypotheses to test the politician's claim.

A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 6 minutes.A random sample of 40 employees were selected and they averaged 6.6 minutes.It is believed that the population standard deviation is 1.7 minutes.The α is set to 0.05.The p-value for this hypothesis test would be ______.

A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team's previously tepid offense historically managed.After a few months,the team owner looks at the data to test the coach's claim.He takes a sample of 36 of the team's games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points.Over the past 10 years,the team had averaged 99 points.What is the value of the appropriate test statistic to test the new coach's claim at the 1% significance level?

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.The parameter to be tested is ___________________________.

If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α =0.05,then the correct conclusion is to ____________________.

To obtain the p-value for a right-tailed test of the population mean,when σ is unknown,we use the Excel's function _________.

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20.In a sample of 200 graduates,30 students have a GPA of 3.00 or below.In testing the university's belief,how does one define the population parameter of interest?

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.Which of the following should be used to develop the null and alternative hypotheses to test this claim?

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 critical value(s)is(are)________.

The null hypothesis in a hypothesis test refers to _____________.

Which of the following are two-tailed tests?

A statistics professor works tirelessly to catch students cheating on his exams.He has particular routes for his teaching assistants to patrol,an elevated chair to ensure an unobstructed view of all students,and even a video recording of the exam in case additional evidence needs to be collected.He estimates that he catches 95% of students who cheat in his class,but 1% of the time that he accuses a student of cheating he is actually incorrect.Consider the null hypothesis,"the student is not cheating." What is the probability of a Type I error?

A professional baseball player changed his throwing motion to increase the velocity of his fastball.Before the change,the player threw his fastball at an average of 91 miles per hour.After the change in his throwing motion,the team watched him throw 64 fastballs with an average speed of 91.75 miles per hour and a standard deviation of 3 miles per hour. a.Specify the null and alternative hypotheses to determine whether the baseball player increased the speed of his fastball. b.Calculate the value of the test statistic and approximate the p-value. c.At the 1% significance level,can you conclude that the baseball player has increased the speed of his fastball? Explain.

The alternative hypothesis typically agrees with the status quo.

The null hypothesis typically corresponds to a presumed default state of nature.

Consider the following hypotheses that relate to the medical field: H_o: A person is free of disease. H_A: A person has disease. In this instance,a Type I error is often referred to as ___________.

You want to test if more than 20% of homes in a neighborhood have recently been sold through a short sale,at a foreclosure auction,or by the bank following an unsuccessful foreclosure auction.You take a sample of 60 homes from this neighborhood and find that 14 fit your criteria.The appropriate null and alternative hypotheses are _______________________.

The hypothesis statement H: µ = 25 is an example of a(an)________ hypothesis.

An analyst conducts a hypothesis test to check whether the mean return for a particular fund differs from 10%.He assumes that returns are normally distributed and sets up the following competing hypotheses: H_o:μ = 10,H_A:μ ≠ 10 Over the past 10 years the fund has had an average annual return of 13.4% with a standard deviation of 2.6%.The value of the test statistic is 4.14 and the critical values at the 5% significance level are−2.262 and 2.262.The correct decision is to ____________________________________.