Mathematics Statistics, Problem Solving

Mathematics Statistics, Problem Solving 1. The Length of a certain species of fish has a normal distribution with mean 50 mm and standard deviation 4.5 mm. A random sample of four fish is drawn and their length X1, X2, X3, and X4, are observed. Calculate the probability that. (3 pts) All four fish have lengths between 51 and 60 mm (3 pts) The mean length of the four fish is between 51 and 60mm (3 pts) Explain why the answer to part A would always be bigger than answer to part b. Answer: a. P (51 X 60) = ( 51-50/4.5) X ( 60 – 50/4.5) = 0.22 X 2.22 = 0.986791 0.587064 = 0.399727 b. Mean of Sampling Distribution = 50 mm Standard Deviation of the Sample = 4.5/sqrt(4) = 4.5/2 = 2.25 t (51) = 51 – 50/ (2.25) = 1 / 2.25 = 0.44 t (60) = 60 – 50/ (2.25) = 4.44 Df = 4 -1 =3 P (51 t 60) = 0.9894 – 0.6551 =0.3343 c. The answer to part A will always be bigger because it is taken from a larger population, whereas the part b is taken from sample, and due to less number of observations, the probability will be less. 2. (3pts) Using computer simulation, several independent random samples each of size n were drawn from a population that has a normal distribution with mean 50 and a standard deviation 9. This means of the samples were then calculated and it was found that 68%of the sample means lies between 48.5 and 51.5. Find the sample size n. Assume that n is large enough for the central limit theorem to hold. Answer: 48.5 – 50 /( 9/sqrtN) X (51.5 -50)/ 9 sqrtN) = 0.68 = 1.5/(9/sqrtN) X 1.5/(SqrtN) = 0.68 = 1.5/(9/sqrtN) = 0.408 = (1.5* SqrtN) = .408 = SqrtN = 0.408/1.5 Sqrt N = 0.272 N = .073984 3. A random variable x has a binomial distribution with n – 100 and p=.45. Using the Normal approximately to the binomial with continuity correction, calculate the following probabilities a. P(X=50) b. P(x60) c. P(40X50) a. 0.048151971 b. 0.000938232 c. 0.682367 4. Recall the population of Ellipticus (copy attached). Using stat crunch, drawindependent random samples of 5 non-mutants and 5 mutants from this population. Then measure the lengths (to the nearest millimeter) of Y1, Y2, Y3, Y4, and Y5 be the lengths of the mutants. Using the data 3 points each A. Obtain a 95 confidence interval for the population mean length ÃŽ ¼Nof non mutants B. Obtain a 95 confidence interval for the population means length ÃŽ ¼M of mutants C. Obtain a 95 confidence interval for the difference in population mean length ÃŽ ¼N-ÃŽ ¼Mbetween non-mutants and mutants 5. The manufacturer of a new prostate cancer drug claims that it has a least 65% cure rate. You are the statistician assigned to validate the claim with data. So you administered the drug on a random sample of 30 patients and proceed with the following test: Let p be the unknown cure rate and let the random variable x be the number of cures among the 30 patients.note that x has a binomial distribution with n-30 and event probablity p. Set up the null hypotheses ho: p0.65 Decision rule: reject ho if the observed number of cures x25 3 point each A. Using statcrunch calculate y(p) for p= .1,.2,.3,.4,.5,.6,.7,.8,.9 B. Graph y(p) versus p using excel (line graph) C. Dicuss briefly how good you this test is based on they(p) above. Answer: The the line is straight sloped line, it shows the there is a constant increase in success with increase in the p or sample D. Construct a test x a for the null hypothesis ho: p=0.65 that will allow you to 10% chance of making a type 1 error (i.e. rejecting a true h0) with maximum probability of rejecting ho y (0.8) when in fact the true state of nature is ha: p=0.8 Test will be based on the changes, with the rejection region of 10% and same the chance of making type I error. The test will consist the sample, with the probability of success change to 0.85

Violence in the Arts  Plato vs. Aristotle Essay - 1285 Words

Violence in The Arts Ââ€" Plato vs. Aristotle Nowadays, it is hard to turn on a television program, catch a movie or buy your younger sibling a video game without encountering a warning for extreme violence. Everyday, our lives are exposed to violence on the screen, whether it is in the latest Sopranos episode or even watching the six oclock news. For quite a while now, people have been demanding that stricter censorship be placed on the media, especially those programs and video games that can easily be obtained by the youth, due to their feelings that this violence can influence people to act out. However, this is not a new idea. Back in ancient Greece, the philosopher Plato believed that exposure to the emotions of the arts†¦show more content†¦Plato perceived the dramas as dangerous, because he felt that they created confusion, miscommunication and ignorance. He also felt that the entire worlds evils came from a defective sense of reality and that these dramas promoted that. For example, take a young child who grew up somewhat isolated from the outside world and whose only outlet to our society is through the media. His steady contact with violent programs (which in the end, show a happy conclusion no matter what happens throughout) may convince him that this type of behavior is normal and accepted. Plato was concerned especially about the influence that drama and even pornography would have on children, because he felt that their minds were not developed to the full extent in order to differentiate between the right and wrong that they see in the dramas. Many people will be quick to agree that a child should not watch a rated R action movie, yet they still allow them to view a Saturday morning cartoon in which the main character gets run over every episode and still comes back the next week. This can create a faulty understanding of reality to a child, as well as an unsuspecting adult, because it does not clarify that death is final. 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Hunger Essay Research Paper Income Poverty free essay sample

Hunger Essay, Research Paper Income Poverty The latest planetary Numberss The World Bank merely updated its estimations of the figure of people life in poorness to 1996 and 1998, utilizing 1993 Buying Power Parities ( PPP ) and family study informations ( see Table 1 and Table 2 ) . The figures for 1998 are preliminary estimations, based on the most recent study informations available ( merely a few studies are available for 1997 and 1998 ) and existent or estimated growing rates in existent private ingestion per capita ; they will be firmed up as new study informations become available. What narrative do the new figures tell? First, both the portion of population and the figure of people populating on less than a dollar a twenty-four hours declined well in the mid-1990s, after increasing in the early 1990s. The same is true for those populating below two dollars a twenty-four hours. But the Numberss rose once more in the wake of the planetary fiscal crisis. The diminutions in the Numberss are about entirely due to a decrease in the figure of hapless people in East Asia, most notably in China. But advancement was partially reversed by the crisis, and stalled in China. In South Asia, the incidence of poorness ( the portion of the population life in poorness ) did diminution reasonably through the ninetiess but non sufficiently to cut down the absolute figure of hapless. The existent figure of hapless people in the part has been lifting steadily since 1987. In Africa, the portion declined and the Numberss increased every bit good. The new estimations indicate that Africa is now the part with the largest portion of people populating below $ 1/day. In Latin America the portion of hapless people remained approximately changeless over the period, and the Numberss increased. In the states of the former Soviet axis, poorness rose markedly-both the portion and the Numberss increased. Table 1. Population populating on less than $ 1 per twenty-four hours and head count index in developing and transitional economic systems, selected old ages, 1987-1998 Regions Population covered by at least one study ( per centum ) Number of people populating on less than $ 1 a twenty-four hours ( 1000000s ) _____________________________________________ www.worldhunger.com

UK and USA during the period 2000

Introduction Real effective exchange rate (REER) is a measure of value of a country’s currency in relation to other major world currencies in the index aimed at countering effects of inflation. Such currencies include euro, US dollar and others. The measure is obtained by looking at the trade balance which is the difference between a country’s imports and exports in comparison with currencies of other countries in the same index.Advertising We will write a custom research paper sample on UK and USA during the period 2000-2010: consumer price index (CPI), unemployment rate, money supply and interest rate specifically for you for only $16.05 $11/page Learn More In the world markets, there usually exist a relationship between the real effective exchange rates and various microeconomic variables such as consumer price index (CPI), unemployment rate, money supply and interest rate. In this paper UK and USA have been considered as the study areas between the years 2000 and 2010. Real effective exchange rate, CPI, Interest Rates, Money supply, Unemployment in US Just like in other countries, US have been experiencing changes in the economic variables such as the real effective exchange rates, consumer price index, interest rates, money supply and the unemployment rates. Generally, these factors have been affected by changes in global economic trends that have also facilitated the government to effect monetary and fiscal policies to mitigate adverse effects. The monetary policy has been regulated by changes in interest rates, devaluation of currencies and regulation in money supply. CPI and Unemployment rates The US economy has had an increasing inflation rates and unemployment rates, 4.0 and 3.4 per cent respectively in year 2000 (Econedlink). This was because the economy was recovering from a serious inflation that had affected the economy towards the end of 1999. The inflation decreased slightly in 2001 to 2.8 as the price s of commodities stabilized (Econedlink). However, the unemployment rate remained high at 4.3 per cent due to lack of enough employment opportunities. The CPI continued to decrease till 2004, as the unemployment rates increased to 5.8 per cent in the same year. Thereafter, the inflation rates increased slightly to 3.4 per cent and unemployment rates decreased slightly to 5.8 per cent (Econedlink). The two variables remained slightly stable, until in 2009 when the world experienced financial crisis. The CPI was at its lowest point at -0.4 per cent while the unemployment rate recorded the highest figure of 9.3 per cent (Econedlink). This scenario coincides with Cencini who illustrates that an inverse correlation exists between inflation and unemployment (41).Advertising Looking for research paper on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More He further adds that an increase in inflation as depicted by increase in CPI c auses reduction in the economic performances that forces employees to be sent home. Sauert asserts that CPI is often included in the interest rates changes and therefore only the unexpected change affect prices (7). During the 2008-2010 financial crises, many employees were rendered jobless thus increasing the number of the unemployed in the country. Money supply, real exchange rate and interest rates As the business cycle changed, the Federal Reserve changed the monetary policy to suite the prevailing economic condition. When the country experiences inflation, the Federal Reserve strives to reduce the amount of money in circulation by increasing exchange rates and vice versa. Despite the several business inflation that has been experienced in the last one decade the US REEL has remind relatively stable compared to other major currencies. According to the global rates report, the US interest rates were decreasing from 2000 to 2004 where the rates decreased from 7 per cent to 1 per c ent in year 2004. This drastic reduction was employed to encourage borrowing by the general public in an attempt to overturn economic slump that was experienced during this time. The interest then increased steadily to 5 per cent in 2005 and 2006. This monetary measure was meant to reduce the amount of money that was in circulation. The large amount of money in circulation caused the consumer price index to go high due to large amount of money that was chasing few goods in the market. Sauret contends that increase in money stock increases chances of inflation in the future (6). Later the economic trend experienced sharp decrease to the current rate of less than 1 per cent as shown in the graph below which was extracted from the global-rates. A graph showing interest rates Advertising We will write a custom research paper sample on UK and USA during the period 2000-2010: consumer price index (CPI), unemployment rate, money supply and interest rate specifically for you for only $16.05 $11/page Learn More Available from http://www.global-rates.com/interest-rates/libor/american-dollar/2000.aspx Despite the many economic turns that have been experienced, the economy has experienced a stable REER over the years as shown by the graph below. The stable REEL has been influenced by a stable strength of the dollar that has been prevailing over the period. The stable value of the dollar has also been attributed to favorable terms of trade that has been experienced by the US. This report also reveals that stability in real effective exchange rate has helped the country to achieve better economic performances. To many economists, stable PEER shows that the economy is performing better compared to other competing economies. In addition it is also right to suggest that the US economy to a great extent managed to deal with inflation and hence managing to contain the value of the dollar. This information is shown by the graph below. Future of US C hina trade.com. Real effective exchange rates, U.S. and China 1993-2010. 13 Jan 2011. 13 Apr 2011. Available from http://www.futureofuschinatrade.com/fact/real-effective-exchange-rates-us-and-china-2000-2010.Advertising Looking for research paper on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More Real effective exchange rate, CPI, Interest Rates, Money supply, Unemployment in UK Although UK is known for its strong economy that is reflected by the strong value of its currency (Sterling Pound), the economy has had its fair share of economic challenges. From 2000 to 2010 the UK economy has been affected by variations in economic variables such the REEL, increased CPI and Interest rates which have resulted to an increase in unemployment rates. Walayat (2010) asserts that these economic variables have been greatly affected by economic cycles such as depression and financial crisis that has been prevalent over the period. The graph below show how various economic variable changes in this period. The graph below shows money supply varied in the period 2009.   Available from http://www.global-rates.com/interest-rates/libor/american-dollar/2000.aspx Interest Rates The UK interest rates were strongly affected by the Credit crisis especially during the 2007-2009, during this period, the UK economy recorded the lowest ever level of interset rates (Walayat). The trend reveal that the growth in the Interest rates have been decreasing between 2000 to 2003 where the rates changed from 6 % to 4.0 and 3.8 per cent respectively, later the interest rates started increasing steadily till the end of 2008 where interest rates were at a peak of 6 per cent. Thereafter, the interest rates dropped drastically to 0.5 percent in 2010 (Walayat). Sauert explains that CPI is usually incorporated in the interest rates and therefore change in interset rates also affects the prices of commodities (93). A decrease in interest rates was accompanied by an increase unemployment rates. As the interest rates dropped, the CPI increased, this reveals that the economy was not performing well and the government strived to boost economic performance by lowering interest rates. This was only possible by employing monitary policies that included economic injections. The government strived to incr ease money supply in order to allow public borrowing. This trend was experienced from 2000 to 2003, as the UK’s economy performances stabilized the real effective exchange rate was increasing as the value of pound increased steadily compared to other major currencies. The trend in economic performance reveals that the UK government does not react in time to changes in interest rates (Walayat). It is evident that when the inflation is at the peak, the interest rate remains in the opposite direction. For instance, since economic forecast reveals the inflation has come to an end, the Bank of England is anticipated to continue raising interest rates to meet this trend. Available from http://www.global-rates.com/interest-rates/libor/american-dollar/2000.aspx Fisher reveals that UK’s CPI has generally been increasing from 2000 to 2010; however, the first three years experienced an intermittent trend of increase and decrease (2). The CPI index for 2000 to 2006 was below six percent but poor economic growth resulted to an increase in the CPI beyond the 2 percent mark. Since CPI measures the changes in the consumer price index, the UK economy was facing a problem in dealing with escalating inflation rate. Since the cost of production was high, firms and other organizations sacked some employees to cut down on the escalating costs. Thus the unemployment level increased steadily, CPI and unemployment moves in the opposite direction (Arnold 128). Bootle (7) reveals that the UK exchange rate has remained high over the stipulated time frame, the sterling pound value increased steadily from 2000 to 2004 whereas; the exchange rate remained high thereafter. The stability in REEL was attributed to the steady foreign exchange conducted by the UK and its economic partners. However, the emergency of financial crisis in 2008-2010 has adversely affected the stability due to the changes in the strengths of other currencies (Fisher 8). The UK economy has been shaken by the recessionary trend that has resulted to various actions that have been taken by the government and other economic institutions. Fisher reports that most firms in UK have strived to retain employees rather than fire them despite the tough economic trend prevailing (4). However, most firms have opted to reduce wage rates and working hours as an attempt to cope with inflation, simply because of the few number of people were getting employed as compared to the those losing their jobs, the unemployment rate was steadily increasing. Agenor (2004) although inflation (CPI) and unemployment rate work in different direction, hyper inflation usually forces unemployment and the CPI to move in the same direction in a situation called inflation trap (215). This has been the situation with the UK economy, whereby it has been experiencing high CPI and high unemployment rates during this period (Bottle 22). Conclusion In both countries the business cycles have affected the entire economic variab les that were in consideration. The main thing that has triggered the variation in these economic variables is inflation and global financial crisis. The most notable one is the economic crisis of 2008-2010 that resulted to high inflation rates that was also accompanied by high unemployment rates. Occurrences of this economic turn prompt the Federal Reserve and the Bank of England to alter the money supply in the countries. On the other hand PEER is mainly affected by the balance of trade and the financial markets. Works Cited Agenor, Pierre-Richard. The economics of adjustment and growth. San Juan, Unitedn States La Editorial, UPR: 2004. Print. Arnold, Roger. Macroeconomics. San Franscisco: Cengage Learning, 2007. Print. Bootle, Roger. The economic and financial outlook. n. d. 12 April, 2011. https://docs.google.com/viewer?a=vq=cache:gMtIWsIVxOMJ:www.thepfs.org /pfsimages/conference/powerpoint_shows/Roger_Bootle.pps+UK %27s+CPI+trend+from+20002010hl=engl=kepid=blsrcid=ADGEESh4y_Lt2 v-6u-5bD38GGBYQOVP21_5wQPpT8LVHIlweO7l27zUi-THSdtCEnauBwjFmAc-3TEDW5sLk8czjDET6CwNAu8ujvJf3qgYtAFtTuF51ICdapcEE9ZGPmcYh9bBqYOVNsig=AHIEtbQTGAfv29wRA4ZzIBy0dMrUj9yQVA Cencini, Alvaro. Inflation and unemployment: contributions to a new macroeconomic.London: Routledge, 1996. Print. Econedlink. Focus on Economic Data. December 2010. 13 April, 2011 http://www.econedlink.org/lessons/index.php?lid=983type=student Fisher, Paul, Why is CPI inflation so high? Liverpool: Bank of England. June 2010. 13 Apr, 2011 http://www.bankofengland.co.uk/publications/speeches/2010/speech438.pdf Future of US China trade.com. Real effective exchange rates, U.S. and China 1993-2010. Jan 2011. 13 Apr, 2011. http://www.futureofuschinatrade.com/fact/real-effective-exchange-rates-us-and-china-2000-2010 Global-Rates. US dollar rates 2000. n.d. 13 Apr, 2011. http://www.global-rates.com/interest-rates/libor/american-dollar/2000.aspx Sauret, Dennis. Do macroeconomic variables have an effect on the US stock market? N orderstedt: Grin, 2002. Print. Walayat, Nadeem. UK Interest Rate Forecast 2010 and 2011. Jan 2010.13 Apr, 2011. http://www.marketoracle.co.uk/Article16450.html This research paper on UK and USA during the period 2000-2010: consumer price index (CPI), unemployment rate, money supply and interest rate was written and submitted by user Cypher to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.