Quantitative Data Analysis Exercise - Assignment Example

Name: Title: QUANTITATIVE DATA ANALYSIS EXERCISE Course: Tutor: Institute: Date due: 1 a The following are some typical sources errors that were likely to occur when this study was carried out. Types of errors Random errors This refers to a statistical fluctuation that occurs because of variations in the elements selected for the sample. This cannot be eliminated. Systematic errors This type of error occurs from some imperfect aspect of the research design or from a mistake in the execution of the research. It is further divided into respondent and administrative errors. The respondent error refers to an error in which a type of sample bias is due to some respondent’s action or inaction of either non response or response bias. Respondent error may arise from people who refuse to cooperate due to perceived amount of work required, intrinsic interest of the topic, and the characteristics of the sample. Response bias is also termed as deliberate falsification; whereby people give false answers to appear intelligent, conceal personal information, and avoid embarrassment. Average -person hypothesis: Individuals may prefer to be viewed as average, so they alter their responses to conform more closely to their perception of the average person. Unconscious Misrepresentation – people may have consciously tried to be truthful but response bias occurred from the question content or some other stimulus. Administrative error These errors may have occurred due to the Interviewer error that is due to field mistakes or deliberate cheating - filling in fake answers or falsifying interviewer Data processing error due to incorrect data entry, computer programming. Sample selection error due to improper sample design or sampling procedure execution. There are 206 Male Illawarra drivers aged 50 and over and 82 out of the total drivers have been fined for a over speeding offence. Male drivers aged between 30-39 caused the highest number of speeding offences. There is a crystal clear trend in the number of over speeding offences increasing from 18 or under to the age group 30-39. In category of Illawara female drivers aged between30-39 were more careful drivers and had the lowest number of speeding offences. In conclusion, the comparing the age set 30-39 for both males and females ladies were very careful when driving. They do not commit speed offences. 1 C Estimation of the total number of Illawarra drivers who have ever been charged with speeding Yes 5 9 24 51 36 Total 125 No 16 21 67 147 121 372 Yes 7 14 38 96 82 Total 237 No 20 26 61 115 124 346 From this data the total number of Illawarra drivers is 1180 and 462 drivers have been charged for speeding offence. The 95% confidence interval for the drivers charged for speeding offence is: lower limit 36.41% and upper limit is 41.97% of the drivers who were charged for speeding offence. 2 (a) This is a type of experimental study, because the study is a type of evaluation that investigate to determine whether a program on had the anticipated causal effect on program participants. The study also has the three key components of an experimental study design that include; a treatment group and a control group, pre-post test design and  random assignment of study participants. 2 (b) Mean  =   44.46809 Median = 46 Proportion obtaining at least 40 = Stem and leaf plot Stem Leaf 0 8 1 7 2 0 4 6 7 7 8 9 3 0 2 2 3 4 5 5 6 8 8 4 1 2 4 6 6 8 9 9 5 0 0 1 2 2 3 8 8 9 6 0 0 1 3 5 7 7 1 1 4 8 8 9 3 Median 2 c No training Mean  =  34 Median 30+38 =68/2 = 34 Proportion obtaining at least 40 = The stem leaf plot Stem leaf 0 8 1 2 0 6 7 3 0 8 4 1 9 9 5 2 2 c ii One hour training Mean  =  50.8 Median = (46+48) / 2=68/2 = 47 Proportion obtaining at least 40 = Stem leaf 2 8 3 2 4 2 4 6 8 5 2 6 0 3 7 8 9 3 2 c iii Two hours training Mean  =  Median = 61 Proportion obtaining at least 40 = stem leaf 3 8 4 5 0 8 9 6 1 5 7 7 1 4 2 c (iv) stem leaf 3 2 3 5 5 4 6 5 8 7 1 8 Mean  =  Median = (35+46)/ 2 = 40.50 Proportion obtaining at least 40 = = 1/2 2 C (v) Mean  =  Median = (34+36)/ 2 = 35 Proportion obtaining at least 40 = = 2/5 stem leaf 1 7 2 4 7 9 3 4 6 4 5 0 1 3 6 0 2(d) According to the above analysis, the best results are obtained when the marketers are trained for two hours. This is because a mean of 60.33 is obtained and has the highest measure of central tendency. The non trained marketers performed poorly with a mean of 34. 2(e) The design or analysis could have been improved by conducting one-way analysis of variance. Analysis of variance (ANOVA) is a technique for analyzing the way in which the mean of a variable is affected or influenced by different types and combinations of factors. Use of One-way analysis of variance is the easiest form. It is an extension of the independent samples t-test and can be applied to compare any number of groups or treatments. This method could be used in the analysis of the effect of amount of training on scores of marketing managers after taking a test. Analysis of variance can be used to test whether there are differences between groups or treatments. In one-way analysis of variance, the variances are used to measure variability. The variance of a set of n values (1, 2, …, n) is given by the following formula: Where: Is the sum of squares. In this analysis, we use the F test where the decision criteria is to fail to reject the null hypothesis if F cal < F tab and reject if otherwise. 2 (f) The conclusion does not change because the best performance will be obtained in the office trained for two hours. The worst performance will be received from the office that was not trained at all. The office receiving 2 hours training has the highest mean of 60.33 points whereas the office that was not trained has the lowest mean of 34 points. I would advise the company to train their officers for a maximum of 2 hours because by doing so, the company increases its performance to a mean of 60.33 points. Training its workforce for more than 2 hours, the company experiences lower performance from its offices i.e. diminishing marginal returns. This is also a waste of company’s resources which should be allocated to more productive areas of the company. References George Woodbury. 2009. An introduction to statistics. Cengage Learning Inc. California, USA Read More