For the following assignment, take out a piece of paper and find the derivative of f(x)=2(3x+5)2

 using two different methods. Label these methods “Method 1” and “Method 2”. 

Scan your work and upload it as a PDF. All work must be visible to receive credit. Or, if there is little to no work to show, you must explain your result. Answers without work or an explanation will not earn points.

For the following assignment , take out a piece of paper and find the derivative of f ( a) = 2/32 – 5 ) using twodifferent methods . Label these methods " Method 1 " and "Method ? "!Scan your work and upload it as a PDF. All work must be visible to receive credit . Or, if there is little to no work to show !you must Explain your result . Answers without work or an explanation will not earn points .

 

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For the following accounts, indicate whether or not there is a debit or credit balance:

 Account Title                Balance Type

Interest income                     

Royalty expense             

Dividend income                 

 

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PHILIP JENKINSOCTOBER 2002 ISSUEU.S.

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Ever since the sexual-abuse crisis erupted in the U.S. Roman Catholic Church in the mid-1980s, with allegations of child molestation by priests, commentators have regularly compared the problems faced by the Church to those it faced in Europe at the start of the sixteenth century, on the eve of the Protestant Reformation—problems that included sexual laxity and financial malfeasance among the clergy, and clerical contempt for the interests of the laity. Calls for change have become increasingly urgent since January, when revelations of widespread sexual misconduct and grossly negligent responses to it emerged prominently in the Boston archdiocese. Similar, if less dramatic, problems have been brought to light in New Orleans, Providence, Palm Beach, Omaha, and many other dioceses. The reform agendas now under discussion within the U.S. hierarchy involve ideas about increased lay participation in governance—ideas of the sort heard when Martin Luther confronted the Roman Catholic orthodoxy of his day. They also include such ideas as admitting women to the priesthood and permitting priests to marry.

Explicit analogies to the Reformation have become commonplace not only among commentators but also among anticlerical activists, among victims’ groups, and, significantly, among ordinary lay believers. One representative expert on sexual misconduct, much quoted, is Richard Sipe, a former monk who worked at the sexual-disorders clinic at Johns Hopkins University and is now a psychotherapist based in California. Over the years Sipe has spoken regularly of “a new Reformation.” “We are at 1515,” he has written, “between when Martin Luther went to Rome in 1510 and 1517 when he nailed his 95 theses on the door in Wittenberg.” That act can reasonably be seen as the symbolic starting point of the Reformation, when a united Christendom was rent asunder.

Historians continue to debate the causes and consequences of the Reformation, and of the forces that it unleashed. Among other things, the Reformation broke the fetters that constrained certain aspects of intellectual life during the Middle Ages. Protestants, of course, honor the event as the source of their distinctive religious traditions; many Protestant denominations celebrate Reformation Day, at the end of October, commemorating the posting of the theses at Wittenberg. And liberal Catholics invoke the word these days to emphasize the urgency of reform—changes both broad and specific that they demand from the Church. Their view is that the crisis, which exposes fault lines of both sexuality and power, is the most serious the Church has faced in 500 years—as serious as the one it faced in Luther’s time.

The first Reformation was an epochal moment in the history of the Western world—and eventually, by extension, of the rest of the world. The status quo in religious affairs was brought to an end. Relations between religions and governments, not to mention among different denominations, took a variety of forms—sometimes symbiotic, often chaotic and violent. The transformations wrought in the human psyche by the Reformation, and by the Counter-Reformation it helped to provoke, continue to play themselves out. This complex historical episode, which is now often referred to simply as “the Reformation,” touched everything. It altered not just the practice of religion but also the nature of society, economics, politics, education, and the law.

Commentators today, when speaking of the changes needed in the Catholic Church, generally do not have in mind the sweeping historical aftermath of the first Reformation—but they should. The Church has developed a fissure whose size most people do not fully appreciate. The steps that liberal Catholics would take to resolve some of the Church’s urgent issues, steps that might quell unease or revolt in some places, would prove incendiary in others. The problem with reform, 500 years ago or today, is that people disagree—sometimes violently—on the direction it should take.

The fact is, we are at a moment as epochal as the Reformation itself—a Reformation moment not only for Catholics but for the entire Christian world. Christianity as a whole is both growing and mutating in ways that observers in the West tend not to see. For obvious reasons, news reports today are filled with material about the influence of a resurgent and sometimes angry Islam. But in its variety and vitality, in its global reach, in its association with the world’s fastest-growing societies, in its shifting centers of gravity, in the way its values and practices vary from place to place—in these and other ways it is Christianity that will leave the deepest mark on the twenty-first century. The process will not necessarily be a peaceful one, and only the foolish would venture anything beyond the broadest predictions about the religious picture a century or two ahead. But the twenty-first century will almost certainly be regarded by future historians as a century in which religion replaced ideology as the prime animating and destructive force in human affairs, guiding attitudes to political liberty and obligation, concepts of nationhood, and, of course, conflicts and wars.

The original Reformation was far more than the rising up of irate lay people against corrupt and exploitative priests, and it was much more than a mere theological row. It was a far-reaching social movement that sought to return to the original sources of Christianity. It challenged the idea that divine authority should be mediated through institutions or hierarchies, and it denied the value of tradition. Instead it offered radical new notions of the supremacy of written texts (that is, the books of the Bible), interpreted by individual consciences. The Reformation made possible a religion that could be practiced privately, rather than mainly in a vast institutionalized community.

This move toward individualism, toward the privatization of religious belief, makes the spirit of the Reformation very attractive to educated people in the West. It stirs many liberal Catholic activists, who regard the aloof and arrogant hierarchy of the Church as not only an affront but something inherently corrupt. New concepts of governance sound exciting, even intoxicating, to reformers, and seem to mesh with likely social and technological trends. The invention of movable type and the printing press, in the fifteenth century, was a technological development that spurred mass literacy in the vernacular languages—and accelerated the forces of religious change. In the near future, many believe, the electronic media will have a comparably powerful impact on our ways of being religious. An ever greater reliance on individual choice, the argument goes, will help Catholicism to become much more inclusive and tolerant, less judgmental, and more willing to accept secular attitudes toward sexuality and gender roles. In the view of liberal Catholics, much of the current crisis derives directly from archaic if not primitive doctrines, including mandatory celibacy among the clergy, intolerance of homosexuality, and the prohibition of women from the priesthood, not to mention a more generalized fear of sexuality. In their view, anyone should be able to see that the idea that God, the creator and lord of the universe, is concerned about human sexuality is on its way out.

If we look beyond the liberal West, we see that another Christian revolution, quite different from the one being called for in affluent American suburbs and upscale urban parishes, is already in progress. Worldwide, Christianity is actually moving toward supernaturalism and neo-orthodoxy, and in many ways toward the ancient world view expressed in the New Testament: a vision of Jesus as the embodiment of divine power, who overcomes the evil forces that inflict calamity and sickness upon the human race. In the global South (the areas that we often think of primarily as the Third World) huge and growing Christian populations—currently 480 million in Latin America, 360 million in Africa, and 313 million in Asia, compared with 260 million in North America—now make up what the Catholic scholar Walbert Buhlmann has called the Third Church, a form of Christianity as distinct as Protestantism or Orthodoxy, and one that is likely to become dominant in the faith. The revolution taking place in Africa, Asia, and Latin America is far more sweeping in its implications than any current shifts in North American religion, whether Catholic or Protestant. There is increasing tension between what one might call a liberal Northern Reformation and the surging Southern religious revolution, which one might equate with the Counter-Reformation, the internal Catholic reforms that took place at the same time as the Reformation—although in references to the past and the present the term “Counter-Reformation” misleadingly implies a simple reaction instead of a social and spiritual explosion. No matter what the terminology, however, an enormous rift seems inevitable.

Although Northern governments are still struggling to come to terms with the notion that Islam might provide a powerful and threatening supranational ideology, few seem to realize the potential political role of ascendant Southern Christianity. The religious rift between Northern and Southern Europe in the sixteenth century suggests just how dramatic the political consequences of a North-South divide in the contemporary Christian world might be. The Reformation led to nothing less than the creation of the modern European states and the international order we recognize today. For more than a century Europe was rent by sectarian wars between Protestants and Catholics, which by the 1680s had ended in stalemate. Out of this impasse, this failure to impose a monolithic religious order across the Continent, there arose such fundamental ideas of modern society as the state’s obligation to tolerate minorities and the need to justify political authority without constantly invoking God and religion. The Enlightenment—and, indeed, Western modernity—could have occurred only as a consequence of the clash, military and ideological, between Protestants and Catholics.

Today across the global South a rising religious fervor is coinciding with declining autonomy for nation-states, making useful an analogy with the medieval concept of Christendom—the Res Publica Christiana—as an overarching source of unity and a focus of loyalty transcending mere kingdoms or empires. Kingdoms might last for only a century or two before being supplanted by new states or dynasties, but rational people knew that Christendom simply endured. The laws of individual nations lasted only as long as the nations themselves; Christendom offered a higher set of standards and mores that could claim to be universal. Christendom was a primary cultural reference, and it may well re-emerge as such in the Christian South—as a new transnational order in which political, social, and personal identities are defined chiefly by religious loyalties.

The first Reformation was a lot less straightforward than some histories suggest. The sixteenth-century Catholic Church, after all, did not collapse after Luther kicked in the door. The Counter-Reformation was moving in a diametrically opposite direction, reasserting older forms of devotion and tradition, and reformulating the Church’s controversial claims for hierarchy and spiritual authority. The Counter-Reformation was not just survivalist and defensive, as is commonly assumed; it was also innovative and dynamic. For at least a century after Luther’s Reformation, in fact, the true political, cultural, and social centers of Europe were as much in the Catholic South as in the Protestant North. The Catholic states—Spain, Portugal, and France—were launching missionary ventures into Africa, Asia, North and South America. By the 1570s Catholic missionaries were creating a transoceanic Church structure: the see of Manila was an offshoot of the archdiocese of Mexico City.

By about 1600 the Catholic Church had become the first religious body—indeed, the first institution of any sort—to operate on a global scale. Even in the Protestant heartlands of Northern and Western Europe—England, Sweden, and the German lands—the heirs of the Reformation had to spend many years discouraging their people from succumbing to the attractions of Catholicism. Conversions to Catholicism were steady throughout the century or so after 1580. It looked as if the Reformation had effectively cut Protestant Europe off from the mainstream of the Christian world. Only in the eighteenth century would Protestantism find a secure and then strategically preponderant place on the global stage, through the success of booming commercial states such as England and the Netherlands, whose political triumphs ultimately contained and in some cases pushed back the earlier empires.

The changes that Catholic and other reformers today are trying to inspire in North America and Europe (and that seem essential if Christianity is to be preserved as a modern, relevant force on those continents) run utterly contrary to the dominant cultural movements in the rest of the Christian world, which look very much like the Counter-Reformation. But this century is unlike the sixteenth in that we are not facing a roughly equal division of Christendom between two competing groups. Rather, Christians are facing a shrinking population in the liberal West and a growing majority of the traditional Rest. During the past half century the critical centers of the Christian world have moved decisively to Africa, to Latin America, and to Asia. The balance will never shift back.

The growth in Africa has been relentless. In 1900 Africa had just 10 million Christians out of a continental population of 107 million—about nine percent. Today the Christian total stands at 360 million out of 784 million, or 46 percent. And that percentage is likely to continue rising, because Christian African countries have some of the world’s most dramatic rates of population growth. Meanwhile, the advanced industrial countries are experiencing a dramatic birth dearth. Within the next twenty-five years the population of the world’s Christians is expected to grow to 2.6 billion (making Christianity by far the world’s largest faith). By 2025, 50 percent of the Christian population will be in Africa and Latin America, and another 17 percent will be in Asia. Those proportions will grow steadily. By about 2050 the United States will still have the largest single contingent of Christians, but all the other leading nations will be Southern: Mexico, Brazil, Nigeria, the Democratic Republic of the Congo, Ethiopia, and the Philippines. By then the proportion of non-Latino whites among the world’s Christians will have fallen to perhaps one in five.

The population shift is even more marked in the specifically Catholic world, where Euro-Americans are already in the minority. Africa had about 16 million Catholics in the early 1950s; it has 120 million today, and is expected to have 228 million by 2025. The World Christian Encyclopedia suggests that by 2025 almost three quarters of all Catholics will be found in Africa, Asia, and Latin America. The likely map of twenty-first-century Catholicism represents an unmistakable legacy of the Counter-Reformation and its global missionary ventures.

These figures actually understate the Southern predominance within Catholicism, and within world Christianity more generally, because they fail to take account of Southern emigrants to Europe and North America. Even as this migration continues, established white communities in Europe are declining demographically, and their religious beliefs and practices are moving further away from traditional Christian roots. The result is that skins of other hues are increasingly evident in European churches; half of all London churchgoers are now black. African and West Indian churches in Britain are reaching out to whites, though members complain that their religion is often seen as “a black thing” rather than “a God thing.”

In the United States a growing proportion of Roman Catholics are Latinos, who should represent a quarter of the nation by 2050 or so. Asian communities in the United States have sizable Catholic populations. Current trends suggest that the religious values of Catholics with a Southern ethnic and cultural heritage will long remain quite distinct from those of other U.S. populations. In terms of liturgy and worship Latino Catholics are strikingly different from Anglo believers, not least in maintaining a fervent devotion to the Virgin Mary and the saints.

European and Euro-American Catholics will within a few decades be a smaller and smaller fragment of a worldwide Church. Of the 18 million Catholic baptisms recorded in 1998, eight million took place in Central and South America, three million in Africa, and just under three million in Asia. (In other words, these three regions already account for more than three quarters of all Catholic baptisms.) The annual baptism total for the Philippines is higher than the totals for Italy, France, Spain, and Poland combined. The number of Filipino Catholics could grow to 90 million by 2025, and perhaps to 130 million by 2050.

The demographic changes within Christianity have many implications for theology and religious practice, and for global society and politics. The most significant point is that in terms of both theology and moral teaching, Southern Christianity is more conservative than the Northern—especially the American—version. Northern reformers, even if otherwise sympathetic to the indigenous cultures of non-Northern peoples, obviously do not like this fact. The liberal Catholic writer James Carroll has complained that “world Christianity [is falling] increasingly under the sway of anti-intellectual fundamentalism.” But the cultural pressures may be hard to resist.

The denominations that are triumphing across the global South—radical Protestant sects, either evangelical or Pentecostal, and Roman Catholicism of an orthodox kind—are stalwartly traditional or even reactionary by the standards of the economically advanced nations. The Catholic faith that is rising rapidly in Africa and Asia looks very much like a pre-Vatican II faith, being more traditional in its respect for the power of bishops and priests and in its preference for older devotions. African Catholicism in particular is far more comfortable with notions of authority and spiritual charisma than with newer ideas of consultation and democracy.

This kind of faith is personified by Nigeria’s Francis Cardinal Arinze, who is sometimes touted as a future Pope. He is sharp and articulate, with an attractively self-deprecating style, and he has served as the president of the Pontifical Council for Inter-Religious Dialogue, which has given him invaluable experience in talking with Muslims, Hindus, Jews, and members of other faiths. By liberal Northern standards, however, Arinze is rigidly conservative, and even repressive on matters such as academic freedom and the need for strict orthodoxy. In his theology as much as his social views he is a loyal follower of Pope John Paul II. Anyone less promising for Northern notions of reform is difficult to imagine.

Meanwhile, a full-scale Reformation is taking place among Pentecostal Christians—whose ideas are shared by many Catholics. Pentecostal believers reject tradition and hierarchy, but they also rely on direct spiritual revelation to supplement or replace biblical authority. And it is Pentecostals who stand in the vanguard of the Southern Counter-Reformation. Though Pentecostalism emerged as a movement only at the start of the twentieth century, chiefly in North America, Pentecostals today are at least 400 million strong, and heavily concentrated in the global South. By 2040 or so there could be as many as a billion, at which point Pentecostal Christians alone will far outnumber the world’s Buddhists and will enjoy rough numerical parity with the world’s Hindus.

The booming Pentecostal churches of Africa, Asia, and Latin America are thoroughly committed to re-creating their version of an idealized early Christianity (often described as the restoration of “primitive” Christianity). The most successful Southern churches preach a deep personal faith, communal orthodoxy, mysticism, and puritanism, all founded on obedience to spiritual authority, from whatever source it is believed to stem. Pentecostals—and their Catholic counterparts—preach messages that may appear simplistically charismatic, visionary, and apocalyptic to a Northern liberal. For them prophecy is an everyday reality, and many independent denominations trace their foundation to direct prophetic authority. Scholars of religion customarily speak of these proliferating congregations simply as the “prophetic churches.”

Of course, American reformers also dream of a restored early Church; but whereas Americans imagine a Church freed from hierarchy, superstition, and dogma, Southerners look back to one filled with spiritual power and able to exorcise the demonic forces that cause sickness and poverty. And yes, “demonic” is the word. The most successful Southern churches today speak openly of spiritual healing and exorcism. One controversial sect in the process of developing an international following is the Brazilian-based Universal Church of the Kingdom of God, which claims to offer “strong prayer to destroy witchcraft, demon possession, bad luck, bad dreams, all spiritual problems,” and promises that members will gain “prosperity and financial breakthrough.” The Cherubim and Seraphim movement of West Africa claims to have “conscious knowledge of the evil spirits which sow the seeds of discomfort, set afloat ill-luck, diseases, induce barrenness, sterility and the like.”

Americans and Europeans usually associate such religious ideas with primitive and rural conditions, and assume that the older world view will disappear with the coming of modernization and urbanization. In the contemporary South, however, the success of highly supernatural churches should rather be seen as a direct by-product of urbanization. (This should come as no surprise to Americans; look at the Pentecostal storefronts in America’s inner cities.) As predominantly rural societies have become more urban over the past thirty or forty years, millions of migrants have been attracted to ever larger urban areas, which lack the resources and the infrastructure to meet the needs of these wanderers. Sometimes people travel to cities within the same nation, but often they find themselves in different countries and cultures, suffering a still greater sense of estrangement. In such settings religious communities emerge to provide health, welfare, and education.

This sort of alternative social system, which played an enormous role in the earliest days of Christianity, has been a potent means of winning mass support for the most committed religious groups and is likely to grow in importance as the gap between people’s needs and government’s capacities to fill them becomes wider. Looking at the success of Christianity in the Roman Empire, the historian Peter Brown has written, “The Christian community suddenly came to appeal to men who felt deserted … Plainly, to be a Christian in 250 brought more protection from one’s fellows than to be a civis Romanus.” Being a member of an active Christian church today may well bring more tangible benefits than being a mere citizen of Nigeria or Peru.

Often the new churches gain support because of the way they deal with the demons of oppression and want: they interpret the horrors of everyday urban life in supernatural terms. In many cases these churches seek to prove their spiritual powers in struggles against witchcraft. The intensity of belief in witchcraft across much of Africa can be startling. As recently as last year at least 1,000 alleged witches were hacked to death in a single “purge” in the Democratic Republic of the Congo. Far from declining with urbanization, fear of witches has intensified. Since the collapse of South Africa’s apartheid regime, in 1994, witchcraft has emerged as a primary social fear in Soweto, with its three million impoverished residents.

The desperate public-health situation in the booming mega-cities of the South goes far toward explaining the emphasis of the new churches on healing mind and body. In Africa in the early twentieth century an explosion of Christian healing movements and new prophets coincided with a dreadful series of epidemics, and the religious upsurge of those years was in part a quest for bodily health. Today African churches stand or fall by their success in healing, and elaborate rituals have formed around healing practices (though church members disagree on whether believers should rely entirely on spiritual assistance). The same interest in spiritual healing is found in what were once the mission churches—bodies such as the Anglicans and the Lutherans. Nowhere in the global South do the various spiritual healers find serious competition from modern scientific medicine: it is simply beyond the reach of most of the poor.

Disease, exploitation, pollution, drink, drugs, and violence, taken together, can account for why people might easily accept that they are under siege from demonic forces, and that only divine intervention can save them. Even radical liberation theologians use apocalyptic language on occasion. When a Northerner asks, in effect, where the Southern churches are getting such ideas, the answer is not hard to find: they’re getting them from the Bible. Southern Christians are reading the New Testament and taking it very seriously; in it they see the power of Jesus fundamentally expressed through his confrontations with demonic powers, particularly those causing sickness and insanity. “Go back and report to John what you hear and see,” Jesus says in the Gospel according to Matthew (11: 4-5). “The blind receive sight, the lame walk, those who have leprosy are cured, the deaf hear, the dead are raised, and the good news is preached to the poor.” For the past two hundred years Northern liberals have employed various nonliteral interpretations of these healing passages—perhaps Jesus had a good sense of the causes and treatment of psychosomatic ailments? But that is not, of course, how such scenes are understood within the Third Church.

Today, as in the early sixteenth century, a literal interpretation of the Bible can be tremendously appealing. To quote a modern-day follower of the African prophet Johane Masowe, cited in Elizabeth Isichei’s A History of Christianity in Africa, “When we were in these synagogues [the European churches], we used to read about the works of Jesus Christ … cripples were made to walk and the dead were brought to life … evil spirits driven out … That was what was being done in Jerusalem. We Africans, however, who were being instructed by white people, never did anything like that … We were taught to read the Bible, but we ourselves never did what the people of the Bible used to do.”

Alongside the fast-growing churches have emerged apocalyptic and messianic movements that try to bring in the kingdom of God through armed violence. Some try to establish the thousand-year reign of Jesus Christ on earth, as prophesied in the Book of Revelation. This phenomenon would have been instantly familiar to Europeans 500 years ago, when the Anabaptists and other millenarian groups flourished. Perhaps the most traumatic event of the Reformation occurred in the German city of Münster in 1534-1535, when Anabaptist rebels established a radical social order that abolished property and monogamy; a homicidal king-messiah held dictatorial power until the forces of state authority conquered and annihilated the fanatics. Then as now, it was difficult to set bounds to religious enthusiasm.

Extremist Christian movements have appeared regularly across parts of Africa where the mechanisms of the state are weak. They include groups such as the Lumpa Church, in Zambia, and the terrifying Lord’s Resistance Army (LRA), in Uganda. In 2000 more than a thousand people in another Ugandan sect, the Movement for the Restoration of the Ten Commandments of God, perished in an apparent mass suicide. In each case a group emerged from orthodox roots and then gravitated toward apocalyptic fanaticism. The Ten Commandments sect grew out of orthodox Catholicism. The Lumpa Church began, in the 1950s, with Alice Lenshina, a Presbyterian convert who claimed to receive divine visions urging her to fight witchcraft. She became the lenshina, or queen, of her new church, whose name, Lumpa, means “better than all others.” The group attracted a hundred thousand followers, who formed a utopian community in order to await the Second Coming of Jesus Christ. Since it rejected worldly regimes to the point of refusing to pay taxes, the Lumpa became increasingly engaged in confrontations with the Zambian government, leading to open rebellion in the 1960s.

Another prophetic Alice appeared in Uganda during the chaotic civil wars that swept that country in the 1980s. Alice Lakwena was a former Catholic whose visions led her to establish the Holy Spirit Mobile Force, also pledged to fight witches. She refused to accept the national peace settlement established under President Yoweri Museveni, and engaged in a holy war against his regime. Holy Spirit soldiers, many of them children and young teenagers, were ritually anointed with butter on the understanding that it would make them bulletproof. When Lakwena’s army was crushed, in 1991, most of her followers merged with the LRA, which is notorious for filling its ranks by abducting children. Atrocities committed by the group include mass murder, rape, and forced cannibalism. Today as in the sixteenth century, an absolute conviction that one is fighting for God’s cause makes moot the laws of war.

The changing demographic balance between North and South helps to explain the current shape of world Catholicism, including the fact that the Church has been headed by Pope John Paul II. In the papal election of 1978 the Polish candidate won the support of Latin American cardinals, who were not prepared to accept yet another Western European. In turn, John Paul has recognized the growing Southern presence in the Church. Last year he elevated forty-four new cardinals, of whom eleven were Latin American, two Indian, and three African. The next time a papal election takes place, fifty-seven of the 135 cardinals eligible to vote, or more than 40 percent, will be from Southern nations. Early this century they will constitute a majority.

It may be true that from the liberal Northern perspective, pressure for a Reformation-style solution to critical problems in the Church—the crisis in clerical celibacy, the shortage of priests, the sense that the laity’s concerns are ignored—seems overwhelming. Poll after poll in the United States and Europe indicates significant distrust of clerical authority and support for greater lay participation and women’s equality. The obvious question in the parishes of the developed world seems to be how long the aloof hierarchy can stave off the forces of history.

From Rome, however, the picture looks different, as do the “natural” directions that history is going to take. The Roman church operates on a global scale and has done so for centuries. Long before the French and British governments had become aware of global politics—and well before their empires came into being—papal diplomats were thinking through their approaches to China, their policies in Peru, their views on African affairs, their stances on the issues facing Japan and Mexico. To adapt a popular activist slogan, the Catholic Church not only thinks globally, it acts globally. That approach is going to have weighty consequences. On present evidence, a Southern-dominated Catholic Church is likely to react traditionally to the issues that most concern American and European reformers: matters of theology and devotion, sexual ethics and gende

 

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1. For the following data,

X

8

6

4

3

4

5

Y

0

1

4

6

6

1

a.Sketch a scatterplot to show the relationship between X and Y. What does the scatterplot tell you?

b.Compute the Pearson correlation.

c.Do these data provide sufficient evidence for a real relationship in the population? Test at the .05 level, two tails.

d.Find the linear equation for predicting Y from X.

e.Conduct a t-test to answer the question: does X significantly predict Y?

f.Calculate the standard error of estimate. What does this measure?

2.To test the effectiveness of a new studying strategy, a psychologist randomly divides a sample of 8 students into two groups, with n=4 in each group. The students in one group receive training in the new studying strategy. Then all students are given 30 minutes to study a chapter from a history textbook before they take a quiz on the chapter. The quiz scores for the two groups are as follows:

Training

6

13

12

9

No Training

1

6

6

3

a.      Perform a t-test to answer the research question: Is the new studying strategy effective? (In other words, whether there is difference in student scores between the two groups.) Use an alpha of .05.

b.     Convert these data into a form suitable for the point-biserial correlation. (use X=1 for training, X=0 for no training, and the quiz scores for Y). Calculate the point-biserial correlation, r, for these data.

c.      Test if the point-biserial correlation, r, is different from zero using an alpha of .05.

d.     Calculate the squared correlation, r2. What does this number mean?

e.      What statement can be made regarding the results of the independent sample t-test comparing two group means and the results t-test of whether the point-biserial correlation is different from zero?

3.A set of n=15 pairs of X and Y values has a Pearson correlation of r=.45 and . If you are using the data as the basis for a regression equation,

a.Find the standard error of estimate.

b.How much error would you expect if the sample size were n=50 instead of n=15?

 

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