Question 1 - Two types of survey methods
There are two types of survey methods that are used when collecting the data provided.
Personal Interview: in this survey method, the respondents are asked a series of questions on face to face basis by an interviewer who collects data from the respondents. The method allows the interviewer to provide collect data as the questions can be explained to the respondents and thus the responses are clear and accurate. Some of the advantages of using this method include that the method is a more accurate method of surveying than most methods, an interviewer can clarify misconceptions from the participants concerning the area of the interview, and the response rate is high when using this method (Lee, 2009). Some of the disadvantages of using this method are that the participants who are the interviewer or interviewee can develop biases which may make the responses untrue or the method is expensive in regards to the expenses associated with training staffs to acquire knowledge and techniques when collecting data.
Self-Administered Survey: When using this survey method, data is collected when the respondents respond to the questions sent to them through the post. Some of the advantages associated with this method include; the respondent can respond to the question asked at the time they find convenient and in the process, they have time to understand the questions before answering them. The survey method is also cost effective. The disadvantages that are associated with this survey method include low expected response rate because not every person has the time to open the posts and some may ignore them. Also, the likelihood of the respondents giving wrong answers is very high (Lee, 2009).
Question 2 - Stratified Random Sampling
When selecting the sample to use, Stratified Random Sampling can be used. This method is very efficient when used because data collected from the survey can be subdivided into subgroups called strata. Then from the strata that have been created, random samples are formed i.e.
Population 1 Population 2 Population 3
- Male - Under 18 years - Business Degree
- Female - 18 - 21 Years - Science Degree
- Transgender - 21 - 30 Years - Engineering Degree
Question 3 - Independent and Dependent Variables
Independent Variables are variables that are controlled in a test to study the effect on a dependent variable. In this case, 'Preparation Time' used in the stratified data sample is continuous data from each student which is denoted as 'X-axis (horizontal), i.e., amount of 'Preparation Time' from students has a large influence on their 'Mark.' The data type is numerical variables, sharing a relationship. Also, the data is quantitative and continuous numerical data.
Dependent Variables, on the other hand, are reliant upon an independent variable. 'Mark' achieved data used in the stratified data sample is discrete data from each student which is denoted as Y axis. i.e., 'Mark' achieved by a student is completely dependent on their 'Preparation Time.' The data type is also numerical variables that are sharing a relationship. Also, the data type is quantitative and continuous numerical data.
Question 4 - The issues faced when collecting the data
Some of the issues that we face when collecting the data include:
Non-Sampling Error: these are errors produced by human errors which may have been avoided if they had been identified or if more attention had been maintained. For example, during selection participants within the target population cannot be included when the survey excludes people without a telephone. During data collection, the respondents may give incorrect information or may misinterpret the terms used in the questionnaire. Also, the error may occur when responses are not obtained from the members of the sample that had been selected for the survey (Yackel and Federer, 2014).
Sampling Error: these are errors in the analysis of data arising from the unrepresentativeness of the sample taken. An example is the population errors which occur when the researcher does not understand who they should survey.
Question 5 - Frequency
|class||intervals frequency||relative frequency||cumulative relative frequency|
Rule: K = 1+3.3(Log10N)
K: Number of Classes;
N: Total Number of Observations
= 100 = 1+3.3 (2.3) = 7.644 8
Largest Value - Smallest Value / Number of Classes
90 - 25 / 8 = 8.125 8
Largest Value - Smallest Value / Number of Classes
100 - 25 / 8 = 9.375 9
The shape of the distribution is negatively skewed to the left. At the same time, data is centered around the mid range. The distribution on the frequency histogram is bell-shaped distribution even though the symmetrical is not perfect. The histogram has a tail extending to the left which means that the frequency histogram is negatively skewed, i.e., skewed to the left.
Relative Frequency Histogram
The Relative Frequency Histogram is also negatively skewed.
Cumulative Relative Frequency Histogram
The cumulative Relative Frequency Histogram is also skewed towards the left.
Question 6 - Trend-line
Trend-line shows that the majority of the points fall close; therefore we can confirm there is a definite positive linear relationship between the two variables. X and Y variables move proportionately in the same direction excluding outliers in the diagram (Yackel and Federer, 2014).
The values from the dependable variable influence marks (Y-Axis);
Preparation Time (X-Axis) is the independent variable, therefore, does not have external influencers.
The line of best fit from the scatter diagram is a linear equation shown below.
y = 0.5831x + 28.984
The equation means that for a unit change in Y to occur, and then one needs X to change with 0.5831 units. For example, when X which is the independent variable increase by one unit, then Y will also increase. As such an increase in; either one unit of X or one unit of Y will cause an increase to the other variable, and the converse is true. The regression is positive among the variables.
|Mode||64 70||49 54|
The preparation time is found on the X-Axis, and it is the independent variable. At the same time, marks are the dependent variable and are in the Y-Axis. The correlation coefficient(R) as shown on the above table is 0.546556431 0.55.
The interpretation that can be given on this correlation coefficient of 0.55 is that there exists a positive linear relationship between the independent variable of preparation time and the dependent variable of marks (Yackel and Federer, 2014). As such, a conclusion can be made that their preparation time has a powerful influence of the marks that a student scores in the exam.
Lee, S. (2009). Understanding Respondent Driven Sampling from a Total Survey Error Perspective. Survey Practice, 2(6), pp.1-6.
Yackel, J. and Federer, W. (2014). Statistics and Society: Data Collection and Interpretation. Journal of the American Statistical Association, 69(347), p.831.
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