Types of Sampling Methods That the Researcher Would Use - Assignment Example

BUSINESS STATISTICS COMPUTER ASSIGNMENT Your name Subject Date BUSINESS STATISTICS COMPUTER ASSIGNMENT Television critics complain that the amount of violence shown on television contributes to violence in our society. A sociologist theorized that people who watch television frequently are exposed to many commercials, which in turn lead them to buy, resulting in increasing debt. To test this belief, a researcher plans to survey a sample of families across the country. Question 1 a) Types of survey methods that the researcher would use. Cross-Sectional Survey: This survey method is used to collect data of a given population at a specified time. For instance this method will be used to explain the relationship between violence and watching television. Elsewhere questionnaires and interviews may be carried out across the countries to express the correlation between the increasing numbers of debts in banks to the commercial adverts in television that cause people to be irrational in their shopping habits. Longitudinal Survey: This survey method collects information over a given period of time. The researcher then gathers the data collected over time, analyze it using computer packages such as excel and present it in tables and graphs to show the trends over a given time. In this case the researcher may decide to monitor two types of children, those who watch television and those who do not, then he collects they weight measures over time and calculate their IBM then draw a graph to show the trend over time. Written Survey: This is the survey method that involves the use of questionnaires to carry out the study. It is a closed-end mode of data collection since it contains specified questions that the correspondent has to fill. It can be used to collect data such as IBM where we need written figures as evidence for the research or for future referenced. Verbal Survey: This method may be used when the researcher aims at getting more information than that of the field work. It is open-ended in nature. For example, the researcher may use oral interviews to collected data on other causes of the increased level of debt other than commercials on television. b) Types of sampling methods that the researcher would use. Stratified Sampling: This is a method of sampling where the researcher divides the populations into small groups or samples called strata, and select from each stratum a sample that will be used for data analysis. For example, the researcher may group the population according to age like Below 18 years, 18-24 years, 25-30 years, 31-40 years and above 41 years, then collect the data from each strata above on violence, IBM and debt. This is an important measure of sampling as different groups of people have different demands of food and different tastes and choice of television channels. Simple Random Sampling: This is a method of sampling where all elements in the population have equal chances of being selected for the population sample. It is an unbiased measure of statistics. The researcher develops a standard criterion on which the sample will be selected as such it is an efficient measure of statistic. In this the researcher may decide to collect weight and IBM to measure obesity after every ten households. In this case every house stands an equal chance of being selected. Cluster Sampling: This is a sampling method where the population is divided into small groups called clusters, and then the sample is selected on a random basis from each cluster. The researcher may use this method in collecting data from different geographical locations. He will divide them into small regions and collect a sample from each region. This eliminates regional bias since some places may be over populated than others. Judgment sampling: This is a non-probability sampling method. The sample is identified primarily by convenience. The researcher selects a sample that he feels represents the population. There is no given criterion since the researcher uses his own knowledge in making the judgments. For example the researcher may decide to collect the sample in urban areas rather than in rural areas since most people in rural areas may not be watching television as much as the people living in urban areas do. c) Variables that the researcher should consider collecting data for the purpose of analysis. Data type for the variables. There are two types of variables that the researcher may consider collecting data for the purpose of analysis. They include: Independent Variables: These are variables that are determined by the researcher, that is, the action that the researcher takes. They may include the following data type: Change in diet in children Change in television watching habits Change in the format of commercial adverts. Dependent Variables: This is the response that the researcher gets as a result of his or her action. It is the final outcome. In this survey they may include: Change in children’s IBM Change in the level of violence Change in the level of debt In summary the choice of an independent variable determines the changes in the dependent variable. Change in children diet →Change in children IBM Change in television watching habits→ Change in the level of violence Change in the format of commercial adverts → Change in the level of debt d) Issues that the researcher may face in this data collection Time Constrains: The researcher may lack adequate time to collect data from the entire population due to a large population. Inadequate finance: The research cost may be too heavy for the researcher to cover solely; as such he may be constrained to inadequate data. Language Barrier: Due to diversity of ethnicity in different places, the researcher may face language barrier challenges and he may be forced to incur an extra cost on hiring interpreters. Sampling error: Since the researcher will use the sample data, the numerical figures calculated on the data collected may be different from those of the actual population thus causing an error. Unwilling correspondent: The interviewee may be unwilling to answer some questions or they may fill ambiguous figures in the questionnaires thus causing an error and limited scope in data collection. QUESTION TWO a) Use of the graphical descriptive methods to present data. Descriptive methods are used to analyze raw data to enable the researcher draw some meaningful conclusions from it. The analysis includes determining the mean, median and mode which are measures of tendency and measures of spread such as standard deviation and variance. The researcher decided the number of classes as 10 and the given interval because he had to consider the following: Variable Range: He had to choose an interval that is approximate to the average variable range. That is the difference between the variables was a major determinant of the interval. Mode of data presentation: The mode of data presentation would cause the researcher to have 10 classes so that they can fit into the graphs as large classes of would not fit into a simple graph. Sample size: The researcher chose an interval of 0-30000 since his sample size composed of figures in tens of thousands. b) Histograms for the variables. The relationship between the two variables. Television is the independent variable since it’s the researcher’s action. Its what the researcher inputs thus it takes the X axis. Debt is the dependent variable since it’s the outcome or the result of the researcher’s action thus it takes the Y axis. From regresion test, there is a significant positive correlation between the two variables. The linear equation that was determined to plot the above graph is: Y=48570.821+2568.482x The gradient of the equation,0.555, is positive thus showing that the two variables, debt and television are positively correlated. QUESTION THREE a) Descriptive variables b) Box plot for the variables Television c) Strength of the relationship Relationship strength is simply the covariance of the variables Correlations Television Debt Television Pearson Correlation 1 .555** Sig. (2-tailed) .000 N 430 430 Debt Pearson Correlation .555** 1 Sig. (2-tailed) .000 N 430 430 The relationship between the two variables can be shown above using the Pearson correlation. It shows that for every 1 change in television, there is a 0.555 change in debt. QUESTION FOUR a) Mean b) Mean at 95% confidence Descriptive Statistics Statistic Bias Std. Error 95% Confidence Interval Lower Upper Television N 430 0 0 430 430 Minimum 6 Maximum 57 Mean 30.43 .01 .48 29.50 31.38 Std. Deviation 9.955 -.002 .305 9.379 10.540 Debt N 430 0 0 430 430 Minimum 20516 Maximum 277234 Mean 126730.32 167.43 2187.65 122724.32 131216.30 Std. Deviation 46049.612 -111.638 1486.008 42986.319 48633.663 Valid N N 430 0 0 430 430 a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples c) Explanation If we increase the confidence interval to 90% the range would increase. QUESTION FIVE a) Test for hypothesis The null hypothesis is that the research hours are 25. The alternative hypothesis is that the research hours are more than 25 We then test for significant at 5% For a two tailed test, at 5% significant level, the critical value is 1.96 The calculated value is Correlations Television Debt Television Pearson Correlation 1 .555** Sig. (2-tailed) .000 N 430 430 Bootstrap Bias 0 .001 Std. Error 0 .031 95% Confidence Interval Lower 1 .495 Upper 1 .616 Debt Pearson Correlation .555** 1 Sig. (2-tailed) .000 N 430 430 Bootstrap Bias .001 0 Std. Error .031 0 95% Confidence Interval Lower .495 1 Upper .616 1 **. Correlation is significant at the 0.01 level (2-tailed). a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples Thus we fail to reject the null hypothesis. Hence we are 95% confident that the television watch hours are 25. b) Hypothesis test for debt The null hypothesis is: The average debt is $150000 The alternative hypothesis is that the average debt is less than $ 150000 This is a one tailed test At 95% significant level, the critical value is 1.65 The calculated value is then given by Correlations Debt Television Debt Pearson Correlation 1 .555** Sig. (1-tailed) .000 N 430 430 Bootstrap Bias 0 .001 Std. Error 0 .031 95% Confidence Interval Lower 1 .493 Upper 1 .616 Television Pearson Correlation .555** 1 Sig. (1-tailed) .000 N 430 430 Bootstrap Bias .001 0 Std. Error .031 0 95% Confidence Interval Lower .493 1 Upper .616 1 **. Correlation is significant at the 0.01 level (1-tailed). a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples Thus since the critical value is greater than the calculated value, we fail to reject the null hypothesis. Hence we are 95% confident that the average debt is $150000 at one tailed test. QUESTION SIX a) Dependent and independent variables Television is the independent variable since it’s the researcher’s action. Its what the researcher inputs thus it takes the X axis. Debt is the dependent variable since it’s the outcome or the result of the researcher’s action thus it takes the Y axis. b) Simple regression model From regresion test, there is a significant positive correlation between the two variables. The linear equation is: Y=48570.821+2568.482x It was derived from the table below Coefficients Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 48570.821 5952.999 8.159 .000 Television 2568.482 185.952 .555 13.813 .000 a. Dependent Variable: Debt c) Test for significance As shown in the table above, there is a significant relationship between the two variables at 95% confidence level d) Debt level calculation The equation determined was: Y=48570.821+2568.482x So since X = 40 Y = 48570.821+2586.482 X 40 =$152030.02 e) Residual of the family 152030.02 – 81708 =$70322.02 f) Measures to assess the quality of the estimate Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate dimension0 1 .555a .308 .307 38342.760 a. Predictors: (Constant), Television b. Dependent Variable: Debt The R value is 55.5%. Thus 55.5% of the regression model is explained by the variables. Thus the model is fit g) Comment on the answer The regression model is fit since the variables are explained. It was therefore suitable to explain the relationship between the two variables h) Debt level for a family whose debt level is 60 Y=48570.821+2568.482x Since X is 60 Y = 48570.821 + 2568.482 X 60 Y= 202679.741 References Babbie Earl R. survey research methods, Belmond OA: wodswork Publication company ;1973 Creswel J.W Research design qualitative and quantitative approaches. Thousands oak CA: Sage 1994 Levy PS and Leme show S. Sampling of population, methods and approaches #rd Edition New york John Wily and Sons Read More