Dependent and Independent Variables - Coursework Example

Several vehicles in a shop is another example (Mann 2010, p. 192). 

Outlier An outlier is a value that falls outside the expected range of values in a data set. The value could be either too small or too large. In a data set of exam results where all students score between 65 percent and 80 percent except one student with 23 percent, the 23 percent is an outlier because it is too small, compared to the other values (Mann 2010, p. 82). 

Mutually exclusive events  These events cannot occur concurrently. Results from a tossed coin are examples because both head and tail cannot appear on a single toast (Mann 2010, p. 154). Question 2: Correlation, regression, and correlation coefficient  Correlation is a statistical measure of the association between variables and shows the strength and direction of the association. Regression, like correlation, is a statistical measure for the association between variables but also offers a model for the relationship. The correlation coefficient is however a measure of the strength of the association between variables (Miller & Yang 2007, p. 428).  Four features of r   One of the features of r is its magnitude which lies between -1 and 1. The measure is also “independent of change of scale and origin” for both the x and y variables of points (Sharma 2009, p. 281). The statistic is also a “geometric mean of two regression coefficients,” and the extent of association between two variables “is symmetric” (Sharma 2009, p. 282). 

Goodness and signs of the correlation  1) The correlation is perfect and positive because it assumes the highest and positive value, + 1.  2) Correlation is strong and positive, owing to its high and positive value of + 0.8. 3) The correlation is weak and positive, because of its positive value which is less than 0.5.   4)   There is no correlation, and can therefore not be defined as either positive or negative.  5) The correlation is weak and negative. 6)   The correlation is strong and negative.  7)   The correlation is perfect and negative. 

Dependent variable and axis Ice cream sales level is the dependent variable, as its value depends on temperature, and it is displayed on the y-axis.  Correlation coefficient The coefficient, based on Excel computation, is 0.9575 Significance The relationship is significant because of the low significance, 1.02*10-6.  Strength of linear relationship The relationship is also strong because the model explains most of the data, 90.85 percent.  Question 3: Probability of crayons on the first spin =1/4 Probability of either crayons or stickers on a second spit =p(C) + p(S)= ¼ + ¼ = ½  Probability of the same two toys =p(C & C) or p(car & car) or p(S & S) or p(D & D) =(1/4*1/4) + (1/4*1/4) + (1/4*1/4)+ (1/4*1/4) = 4(1/16)= ¼   Each arrow represents a probability of ¼ Question 4: Several T-shirts are equal to the product in quantities in every category.  Required number of shirts = materials* colours* size* number per type= 2*12*5*20 = 2400 shirts Increased varieties  Number of t-shirts= materials* sleeve type* colours* size* number per type  =3*3*12*5* 20= 10800 shirts Professional committee 

Forming the committee requires a selection of ten members, by profession, and these can form the committee in any order. The combination will help in determining possible arrangements from each profession, followed by the multiplication of the arrangements. The 10 members are arranged without regard to order and without replacement.   Therefore, =6P4*8P3*5P3 =  360*336*60 =7257600 possible committees.  (Prasad, Rao, T., & Rao, M. 2009, p. 276- 276) Question 5: Expressions  Rate charged Rate= (change in y/change in x)x+ c Rate= 60*hours+ 100 Overhead  Overhead= 30*Hours+ 250 Constants, coefficients, and variables For the rate charges, 100 is the constant, 60 is the coefficient, and amount and time are variables. For the overhead, 250 is the constant, 30 is the coefficient, and amount and time are variables.  Required hours for break-even Break-even occurs when cost equals revenues, and is, therefore, the point of intersection. Hours are five and the coordinate is (5, 400).  Question 6: Equations and rationale for the use Sample variance Sample variance= {∑(xi-µ)}/n-1 Where in is the sample size and xi is the ith variable.  Population variance Population variance (S2)= {∑(xi-µ)}/n Where in is the sample size and xi is the ith variable.  Standard deviation  Standard deviation= S= [{∑(xi-µ)}/n]1/2 The statistics are used to measure the dispersion of data in a set (Weinberg & Abramowitz 2008, p. 231). 

Question 7: Hypothesis  HO: µ= 440, current performance is typical HA: µ≠ 440, current performance is not typical This is a two-tailed test.  Zc= (x- µ)/standard error = (425-440)/(2500.5/150.5) =-15/(4.82) = -3.67 But Ztable= 1.95  ǀZcǀ> Ztable and the null hypothesis is rejected. The current performance is therefore not typical (Mann 2010, p. 390- 398). Read More