Within a complex machine such as a robotic assembly line, suppose one particular part glides along a straight track. A control system measures the average velocity of the part during each successive time interval t0=t00,t0=t00, compares it with the value vcvc it should be, and switches a servo motor on and off to give the part a correcting pulse of acceleration. The pulse consists of a constant acceleration amam applied for time interval tm=tm0tm=tm0 within the next control time interval t0t0 . As shown in Figure P2.30P2.30 , the part may be modeled as having zero acceleration when the motor is off (between tmtm and t0).t0). A computer in the control system chooses the size of the acceleration so that the final velocity of the part will have the correct value vcvc Assume the part is initially at rest and is to have instantaneous velocity vcvc at time t0.t0. (a) Find the required value of amam in terms of vcvc and tmtm (b) Show that the displacement xx of the part during the time interval t0t0 is given by x=vc(t00.5tm).x=vc(t00.5tm). For specified values of vcvc and t0,t0, (c) what is the minimum displacement of the part? (d) What is the maximum displacement of the part? (e) Are both the minimum and maximum displacements physically attainable?

During the 2003 season, Major League Baseball took steps to speed up the play of baseball games in order to maintain fan interest ( CNN Headline News, September 30,2003 ). The following results come from a sample of 60 games played during the summer of 2002 and a sample of 50 games played during the summer of 2003.2003. The sample mean shows the mean duration of the games included in each sample. 2002Seasonn1=60x1=2hours,52minutes2003Seasonn2=50x2=2hours,46minutes2002Season2003Seasonn1=60n2=50x1=2hours,52minutesx2=2hours,46minutes a. A research hypothesis was that the steps taken during the 2003 season would reduce the population mean duration of baseball games. Formulate the null and alternative hypotheses. b. What is the point estimate of the reduction in the mean duration of games during the 2003 season? c. Historical data indicate a population standard deviation of 12 minutes is a reasonable assumption for both years. Conduct the hypothesis test and report the pp -value. At a .05 level of significance, what is your conclusion? d. Provide a 95%95% confidence interval estimate of the reduction in the mean duration of games during the 2003 season. e. What was the percentage reduction in the mean time of baseball games during the 2003 season? Should management be pleased with the results of the statistical analysis? Discuss. Should the length of baseball games continue to be an issue in future years? Explain.

Will improving customer service result in higher stock prices for the companies providing the better service? "When a company's satisfaction score has improved over the prior year's results and is above the national average (currently 75.77 , studies show its shares have a good chance of outperforming the broad stock market in the long run" (Business-Week, March 2,20092,2009 ). The following satisfaction scores of three companies for the 4th quarters of 2007 and 2008 were obtained from the American Customer Satisfaction Index. Assume that the scores are based on a poll of 60 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 6 points in each case. CompanyRite AidExpediaJC Penney2007Score7375772008Score767778Company2007Score2008ScoreRite Aid7376Expedia7577JC Penney7778 a. For Rite Aid, is the increase in the satisfaction score from 2007 to 2008 statistically significant? Use =.05=.05 . What can you conclude? b. Can you conclude that the 2008 score for Rite Aid is above the national average of 75.77 Use =.05=.05 c. For Expedia, is the increase from 2007 to 2008 statistically significant? Use =.05=.05 . d. When conducting a hypothesis test with the values given for the standard deviation, sample size, and ,, how large must the increase from 2007 to 2008 be for it to be statistically significant? e. Use the result of part (d) to state whether the increase for JC Penney from 2007 to 2008 is statistically significant.

Ex and United Parcel Service (UPS) are the world's two leading cargo carriers by volume and revenue (The Wall Street Journal, January 27,2004 ). According to the Airports Council International, the Memphis International Airport (FedEx) and the Louisville International Airport (UPS) are 2 of the 10 largest cargo airports in the world. The following random samples show the tons of cargo per day handled by these airports. Data are in thousands of tons. Memphis9.18.3Louisville4.72.215.19.15.04.18.86.04.22.610.05.83.33.47.512.15.57.010.59.3Memphis9.115.18.810.07.510.58.39.16.05.812.19.3Louisville4.75.04.23.35.52.24.12.63.47.0 a. Compute the sample mean and sample standard deviation for each airport. b. What is the point estimate of the difference between the two population means? Interpret this value in terms of the higher-volume airport and a comparison of the volume difference between the two airports. c. Develop a 95%95% confidence interval of the difference between the daily population means for the two airports.

The Tire Rack, America's leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and conditions in which they drive. In addition, they have maintained an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The data shown below show survey ratings (1(1 to 10 scale with 10 the highest rating) for two all-season passenger tires, the Dunlop SP60SP60 and the Michelin MX4 (Tire Rack website, April 18,2008).18,2008). a. Formulate the hypotheses that can be used to determine whether the sample data sup- port the hypothesis that the mean rating for Dunlop SP60 tires is greater than the mean rating for Michelin MX4 tires. b. What is the point estimate of the difference between the means for the two populations? c. Compute the pp -value for the hypothesis test. d. At=.05,At=.05, what is your conclusion?

Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2010(2010 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant AA has 10 years of experience, whereas consultant BB has 1 year of experience. Use =.05=.05 and test to see whether the consultant with more experience has the higher population mean service rating. a. State the null and alternative hypotheses. b. Compute the value of the test statistic. c. What is the pp -value? d. What is your conclusion?

Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in PGA tournaments are shown in the following table (Golfweek, February 14,2009,14,2009, and February 28,2009).28,2009). Suppose you would like to determine if the mean score for the first round of a PGA Tour event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down? a. Use =.10=.10 to test for a statistically significantly difference between the population means for first- and fourth-round scores. What is the pp -value? What is your conclusion? b. What is the point estimate of the difference between the two population means? For which round is the population mean score lower? c. What is the margin of error for a 90%% confidence interval estimate for the difference between the population means? Could this confidence interval have been used to test the hypothesis in part (a)? Explain.

In recent years, a growing array of entertainment options competes for consumer time. By 2004,2004, cable television and radio surpassed broadcast television, recorded music, and the daily newspaper to become the two entertainment media with the greatest usage (The Wall Street Journal, January 26,200426,2004 ). Researchers used a sample of 15 individuals and collected data on the hours per week spent watching cable television and hours per week spent listening to the radio. a. Use a .05 level of significance and test for a difference between the population mean usage for cable television and radio. What is the pp -value? b. What is the sample mean number of hours per week spent watching cable television? What is the sample mean number of hours per week spent listening to radio? Which medium has the greater usage?

Mutual funds are classified as load or nonoload funds. Load funds require an investor to pay an initial fee based on a percentage of the amount invested in the fund. The no-load funds do not require this initial fee. Some financial advisors argue that the load mutual funds may be worth the extra fee because these funds provide a higher mean rate of return than the no-load mutual funds. A sample of 30 load mutual funds and a sample of 30 no-load mutual funds were selected. Data were collected on the annual return for the funds over a five-year period. The data are contained in the data set Mutual. The data for the first five load and first five no-load mutual funds are as follows. a. Formulate H0H0 and H_{\text{asuchthatrejectionof}H_{0}\text{leadstotheconclusionthattheloadmutualfundshaveahighermeanannualreturnoverthefive-yearperiod.b.Usethe60mutualfundsinthedatasetMutualtoconductthehypothesistest.WhatistheH_{\text{asuchthatrejectionof}H_{0}\text{leadstotheconclusionthattheloadmutualfundshaveahighermeanannualreturnoverthefive-yearperiod.b.Usethe60mutualfundsinthedatasetMutualtoconductthehypothesistest.Whatisthepvalue?Atvalue?At\alpha=.05,$ what is your conclusion?

A study reported in the Journal of Small Business Management concluded that self- employed individuals do not experience higher job satisfaction than individuals who are not self-employed. In this study, job satisfaction is measured using 18 items, each of which is rated using a Likert-type scale with 1515 response options ranging from strong agreement to strong disagreement. A higher score on this scale indicates a higher degree of job satisfaction. The sum of the ratings for the 18 items, ranging from 18 to 90 , is used as the measure of job satisfaction. Suppose that this approach was used to measure the job satisfaction for lawyers, physical therapists, cabinetmakers, and systems analysts. The results obtained for a sample of 10 individuals from each profession follow. At the =.05=.05 level of significance, test for any difference in the job satisfaction among the four professions.

In early 2009,2009, the economy was experiencing a recession. But how was the recession affecting the stock market? Shown are data from a sample of 15 companies. Shown for each company is the price per share of stock on January 1 and April 30 (The Wall Street Journal, May 1,20091,2009 ). a. What is the change in the mean price per share of stock over the four-month period? b. Provide a 90%% confident interval estimate of the change in the mean price per share of stock. Interpret the results. c. What was the percentage change in the mean price per share of stock over the four- month period? d. If this same percentage change were to occur for the next four months and again for the four months after that, what would be the mean price per share of stock at the end of the year 2009??

One of the biggest changes in higher education in recent years has been the growth of online universities. The Online Education Database is an independent organization whose mission is to build a comprehensive list of the top accredited online colleges. The following table shows the retention rate (Y0)(Y0) and the graduation rate (Y/6)(Y/6) for 29 online colleges (Online Education Database website, January 2009 ). a. Develop a scatter diagram with retention rate as the independent variable. What does the scatter diagram indicate about the relationship between the two variables? b. Develop the estimated regression equation. c. Test for a significant relationship. Use =.05=.05 . d. Did the estimated regression equation provide a good fit? e. Suppose you were the president of South University. After reviewing the results, would you have any concerns about the performance of your university as compared to other online universities? f. Suppose you were the president of the University of Phoenix. After reviewing the results, would you have any concerns about the performance of your university ac compared to other online universities?

Pew Research Center is a nonpartisan polling organization that provides information about issues, attitudes, and trends shaping America. In a recent poll, Pew researchers found that 47%% of American adult respondents reported getting at least some local news on their cell phone or tablet computer (Pew Research website, May 14,2011).14,2011). Further findings showed that 42%% of respondents who own cell phones or tablet computers use those devices to check local weather reports and 37%% use the devices to find local restaurants or other businesses. a. One statistic reported concerned using cell phones or tablet computers for local news. What population is that finding applicable to? b. Another statistic concerned using cell phones or tablet computers to check local weather reports and to find local restaurants. What population is this finding is applicable to? c. Do you think the Pew researchers conducted a census or a sample survey to obtain their results? Why? d. If you were a restaurant owner, would you find these results interesting? Why? How could you take advantage of this information?