Statistics in a Real-World Context - Essay Example

Running Head: STATISTICS Statistics of the of the Statistics Assignment Q1a. Probability Tree Showing Possible Outcome Let suppose in total 10 CDs, 3 are classical i.e. C1, C2, and C3, 2 are jazz i.e. J1 and J2 and Rest of 5 are pop i.e. P1, P2, P3, P4 and P5 b. P (Anna choosing 2 pop CDs) Solve it by using combination formula nCr = Computation P (2 pop CDs) = = = = 0.222 So, Probability that Anna choosing 2 pop CDs would be 0.222 or 22%. c. P (2 different types of CD being chosen) P (2 different types of CDs) = = = = = = 0.688 So, probability of 2 different types of CD being chosen would be 68.8%. d. Probability in real world context Probability as a general concept can be defined as the chance of an event occurring. In addition to being used in games of chance, probability is used in different real life fields like insurance, investments, and weather forecasting, and in various areas. Weather Forecasting - Let us suppose that we would like to go on a picnic tomorrow morning, and the weather forecasting report says that the possibility of raining would be 80%. Do we ever wonder where that 80% came from Forecasting like these can be measured by the group who employee in the National Weather Service when they seems at all other days in their historical record that have the same weather characteristics (humidity, pressure, temperature, etc.) and conclude that on 80% of comparable days in the history, it rained. According to basic probability we divide the figure of favourable outcomes by the total number of possible outcomes in our sample space. If we're observing for the chance it will rain, this will be the number of days in our record that it rained divided by the total number of similar days in our record. If our meteorologist has data for 100 days with similar weather conditions, and on 80 of these days it rained (a favourable outcome), the probability of rain on the next similar day is 80/100 or 80%. In view of the fact that a 50% probability means that an experience is as likely to happen as not, 80%, which is greater than 50%, means that it is more likely to rain than not. But what is the probability that it won't rain Keep in mind that because the favourable outcomes represent all the possible ways that an event can occur, the sum of the different probabilities must equal 1 or 100%, so 100% - 80% = 20%, and the probability that it won't rain is 20%. 2. The table below gives the marks of 15 students in tests in 2 subjects: Students 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Maths 29 45 27 19 39 46 25 38 39 43 49 21 38 46 37 Science 36 42 31 26 42 41 25 41 40 40 43 23 39 45 38 a. Scatter graph of the maths and science scores with best fitted line The following scatter plot with a fitted line shows that there is a positive relationship b/w selected 15 student's maths and science scores. Part 2b will be the evidence to prove this hypothesis that student's math scores will be positively related to their science scores. Correlation coefficient (r = + 0.936) this magnitude shows that it's highly correlated and the positive sign shows that there is a positive correlation between the variables. So we conclude that as one variable increases other one will also increases. b. Comment on the position of the line of best fit and any correlation between the scores. Although one objective of correlation is a line fitted to the data, this line is not used to predict an unknown value of one variable when given a value of the other variable; it simply shows the relationship between the two variables. This best-fit line is the one that minimizes the sum of squared deviations between the points and the line, measured vertically (along the Y axis). The Bivariate Correlations procedure computes Pearson's correlation coefficient. Correlations measure how variables or rank orders are related. Before calculating a correlation coefficient, screen your data for outliers (which can cause misleading results) and evidence of a linear relationship. Pearson's correlation coefficient is a measure of linear association. Two variables can be perfectly related, but if the relationship is not linear, Pearson's correlation coefficient is not an appropriate statistic for measuring their association. Computation Pearson Correlation Maths Science Maths 1 0.936 Science 0.936 1 The correlation coefficient states that maths and science scores, these are highly positive correlated variables. As far as correlation coefficient approaches to +1 we can say that there is strong highly positive correlation between the variables, it mean as for as one variable increases the value of other also increases, or vice versa. The correlation coefficient for the relationship between maths and science scores in selected students is +0.936. This means that when the maths scores increases, the science scores in selected 15 students are also tends to increase. It is also important to note that the correlation coefficient only measures linear relationships. A meaningful nonlinear relationship may exist even if the correlation coefficient is 0. The coefficient of determination, r 2, is also a useful tool because it gives the proportion of the variance (fluctuation) of one variable that is predictable from the other variable. It is a measure that allows us to determine how certain one can be in making predictions from a certain model/graph. It is such that 0 M Taking a sample size of n = 30 students, for testing this hypothesis. Mean and range of the students heights are the most relevant measures of average and spread respectively. Two sample hypothesis testing would be the appropriate way of presenting data and comparing male and female results. 5a. what proportion are rejected Given that = 100g and = 2g. Computation P (99 < < 105) = P = P = (2.5) - (-0.5) = 0.9938 - 0.3085 = 0.6853 or 68.53% About 0.6853 proportion are rejected in this situation. b. The minimum weight would be 75g. c. The Bureau of census reports the mean income of households in its annual publication. To obtain complete population data - the income of households - would be extremely expensive and time consuming. It is also unnecessary, because accurate estimates for the mean income of all households can be obtained from the mean income of sample of such households. Once the sample the been taken, the Census Bureau can compute the sample mean income of the 72,000 households obtained. Using the sample men income we can estimate the population men income of all households. And the unit of sample income is the same as unit of population income. Work Cited Brannen, Julia (1992) Combining Qualitative and Quantitative approaches: An overview. In Julia Brannen (Ed.), Mixing Methods: Qualitative and Quantitative research, Aldershot: Avebury pg (3-37) Guba, E.G,and Lincoln, Y.S (1998) Compeating paradigms in Qualitative research in Denzin, N.K. Lincoln, Y.S (eds) The Landscape of Qualitative Research Theories and Issues, SAGE, Thousand oaks, pg(s) 195-220 Higgs J, ed (1997) Qualitative Research: Discourse on Methodologies Hampden Press, Sydney. Higgs, J and Adams, R (1997) Seeking Quality in Quantitative research, in J Higgs 9Ed) qualitative research: Discourse on methodologies (1) Hampton press Sydney. McCallough dick, Quantitative vs. qualitative marketing (2003) available at www.macronic.com/html/art/s_qua.html (accessed on 4/05/2003) Redmond A, Keenan A-M and Landorf K (2000) 'Horses for courses': the differences between quantitative and qualitative approaches to research. Australasian Journal of Podiatric Medicine. Vol 34 no 1 pg(s) 5-14 (accessed on 4/05/2003) Read More