1. The Chair of the East Asian languages department at a local university is now mandating that first-year students enroll in conversation-only language laboratories in addition to the typical lecture-based classes that emphasize grammar and vocabulary drills. The purpose of the conversation laboratory sessions is to improve students' comprehension and speaking skills. They are conducted on a weekly basis, one hour per session. After the first semester, the Chair wants to conduct a test to determine if students who participate in the conversation classes perform better than students who have not. The average nal examination result for students from earlier academic years, when no conversation-only laboratories were available, has been 72 (out of a possible of 150). How should the null and alternative hypotheses
be expressed?

(a) What inference can be drawn if H₀ is rejected?

(b) What if H₀ is not rejected?

(a) If a Type I error is committed, what mistake is being made?

(b) If a Type II error is committed, what mistake is being made?

4. The U.S. Department of Homeland Security has faced mounting criticism over the length of time departing passengers are now forced to wait while clearing security (e.g., searches, metal detectors, passport control) as they prepare to board commerical  flights. In view of this, the Homeland Security Department manager at Newark International Airport has taken several measures that he hopes speed up the process of getting air passengers through the Airport and onto their plane. Compounding
the challenge is the fact that the number of passengers passing through Newark has been steadily increasing every month for several years. The Department manager wants to know if the average passenger security clearance waiting time has changed from 39 minutes it was the last time it was measured. If the measures have been successful, the waiting time should be shorter; if the passenger volume at Newark has overwhelmed any measures that might be taken, the waiting time may be longer. How should the Department manager express the null and alternative hypotheses?

(a) What inference can be drawn if H0 is rejected?

(b) What if H₀ is not rejected?

(a) For this testing situation, what is a Type I error?

(b) What is a Type II error?

7. In recent years, applications to the Ph.D. programs of 10 selected schools of engineering in the U.S. included 18,522 from foreign students. However, in early 2017, a group of administrators representing American research universities expressed concern that the number of applications to their Ph.D. programs from non-U.S. students might decline. In January 2017, President Donald Trump announced a new policy designed to restrict and otherwise discourage applications from overseas students wishing to pursue Ph.D. degrees in engineering and science. If we wish to test whether his policies are having the intended effect of discouraging and reducing overseas applicants, how should the null and alternative hypotheses be expressed?

(a) What inference can be drawn if H₀ is rejected?

(b) What if H0 is not rejected?

(a) Describe a Type I error.

(b) What is a Type II error.

10. The public school board responsible for a district in the U.S. state of Louisiana has decided to take on the obesity problem among high school students by introducing a healthier diet (lower fat, sugar, and salt; more vegetables, less fried food) into the school lunch program. Last year, 19% of adolescent youths, aged 15 to 18 years, were designated obese. In an effort to monitor the success of the new school lunch program, school offcials have decided to collect data from all schools in the district at the end of the first year of implementation. If we let p be the percentage of students classified as obese, how should school officials frame the null and alternative hypotheses ?

(a) What inference can be drawn if H₀ is rejected?

(b) What if H₀ is not rejected?

(a) What is a Type I error?

(b) What is a Type II error?

13. The percent of purchases made online (rather than at brick-and-mortar retail locations) is increasing each year as more consumers find the internet shopping experience more convenient and economical than that at malls or big-box retail locations. Naturally, this trend poses challenges to traditional brick-and-mortar retailers of all kinds in all developed economies. A Canadian business school professor stated recently that she believed that at least 50% of consumer purchases are now made online. If we were to collect data on the shopping habits from a sample of Canadian households to determine if most consumer purchases (i.e., more than 50%) are now made online, how should we express the null and alternative hypotheses? Let p be the percent of purchases that are made online.

(a) What inference can be drawn if H₀ is rejected?

(b) What if H₀ is not rejected?

(a) What does a Type I error mean?

(b) What is a Type II error?

16. On April 23, 2017, French citizens cast their ballots for the candidates who would face one another in the French Presidential election to be held two weeks later. From the field of four, the two candidates who emerged successful are Emmanuel Macron and Marine Le Pen. Political scientists would like to predict which of the two candidates will ultimately succeed to the Presidency, and so they turn to political polling and statistical analysis to guage the early sentiment among the French voting public. Since both candidates are considered unconventional|neither has run for the Presidency in the past and neither represents one of France's traditional political parties|the early guess is that each candidate has a 50% chance of winning. How should the null and alternative hypotheses tests be structured? Let p be the proportion of voters favoring Marine Le Pen.

(a) What inference can be drawn if H₀ is rejected?

(b) What if H₀ is not rejected?

(a) Describe a Type I error.

(b) What is a Type II error.

(a) What is a Type I error?

(b) What is a Type II error?

(c) Although in a criminal trial we do not establish values for α and β, we would ideally like to set the value of lower than for β. Why?

20. Referring to the Agrico example (Section 10.1), suppose the quality-control manager decides that while Agrico does not want to under ll its packages, neither does it wish to overfill. Clearly, giving away product in overfilled packages costs Agrico money, and provides little or no goodwill among customers who are unaware they are reaping a windfall in free bran flakes. Suppose that the sample size is adjusted upward to n = 100 and α is reset to 0.10. Using the six-step hypothesis-testing framework, test H0 : µ ≤375 against Ha : µ>375. Recall that σ = 22.5. Suppose the sample of n = 100 provides a mean weight of 377.50 grams. What is the p-value?

(e) Since x̄ = 377.50,

(f) Since z = 1.111<1.282 (and thus does not fall in the RR), we do not reject H₀. We cannot conclude from the evidence that Agrico is over lling its packages.

21. Family physicians in Tampa, Florida reportedly earn an average annual salary of $141. 300. Suppose we conduct a survey on a sample of n = 64 family physicians from New Orleans, Louisiana to test whether their mean annual salary is different from the reported mean of $141, 300 in Tampa, and find that the sample mean is $138, 000. Assume σ = $18, 000. At the level of α = 0.01, use the six-step framework
to test H0 : µ = 141, 300; against Ha : µ0 ≠ 141, 300. What is the p-value?

(e) Since x̄ = 138, 000,

(f) Since z = 1.47<2.576 (and thus does not fall in the RR), we do not reject H₀. We cannot conclude from the evidence that New Orleans physician salary is different from Tampa physician salary.

22. Because two Australian students are planning to attend the University of London next academic year, they are searching for a  at in the WC1 district of the city, a neighborhood that offers many amenities to the University's students. Even though they plan to share the apartment, they are unwilling to pay more than $4000 per month for rent. As a preliminary step, they want to make sure that the neighborhood they have selected is a realistic choice, given this budgetary constraint, before committing to this particular area. Suppose they search online for rental properties and compile a list of 70 flats in the Russell Square vicinity, along with each property's monthly rent. Use the housing data (from the companion website) to test H0 : µ ≥ 4000 against H_a : µ < 4000 at α = 0.10. The variable name is rent.

23. The research director at a major advertising agency believes that people are watching more (rather than less) television during the 2-day holiday period from New Year's Eve through New Year's Day. Before the 2008 financial crisis, when many people traveled during the holidays, the average amount of television viewing during the New Year period was 10 hours. The research director would like to know if
the amount of television viewing has increased as more people decide to stay home over the holidays rather than travel. Assume that television viewing data have been collected across 100 households during the most recent New Year's holiday period. Use the tv hours data (from the companion website), and test H0 : µ ≤ 10 against H_a : µ >10 at the α = 0.01. The variable name is hours.

24. The student newspaper at a large business school claims that 55% of graduating students have an offer of employment even before they graduate. The Offce of Student Affairs decided to investigate this claim to see whether it is true. When they carried out the survey, they found that 321 of 535 graduating students reported that they have a job o er. At a level of α = 0.10, use the six-step framework to test
H₀ : p = 0.55 against H_a : p ≠ 0.55. What is the p-value?

(e) Since p = 321/535 = 0.60,

(f) Since z = 2.32>1.645, we reject H₀ and conclude that the percent of students having jobs upon graduation differs from (and exceeds) 0.55.

25. While campaigning for higher political office during a recent election, a certain candidate claimed that \at least 75% of voters want the country to end all foreign aid to all countries." When a polling organization conducted a survey to investigate this claim, they found that 242 out of a sample of n = 346 expressed agreement with the statement. At a level of α = 0.02, use the six-step framework to test
H₀ : p ≥ 0.75 against H_a : p<0.75. What is the p-value?

(f) Since z = -2.1727< - 2.054, we reject H₀ and conclude that the percent of people favoring elimination of foreign aid is less than 0.75.

26. An Italian farmer who grows and packs agricultural produce for the export market claims that one of his packages contains 750 grams of tomatoes. To ensure that the company consistently meets this standard, the manager conducts a study to test H₀ : µ ≥750 against H_a : µ<750. Based on previous studies, σ = 25. What sample size should the manager use if he wants a 0.90 probability of identifying when the mean weight falls short of 750 grams by 10 grams? Let α = 0.01.