Survey Method and Sampling Method
A sociologist develops a theory that frequent watching of television exposes individuals to many commercials, which lead people to buy the goods and in turn lead to increased debt. To justify the claim, he carries out a survey on a sample of 400 individuals across the country.
The purpose of the assignment is to carry out statistical analysis to the sociologists finding and come-up with a solution of whether or not there is a relationship between the television watched and the debt as a result of watching commercials.
Solutions
- The surveyor could have used an interviewer administered survey inform of personal interview or telephone call. This method of survey would help the interviewer get a one-one answer from the respondent of how much television hours they have and how much they borrow based on the commercials they watch. Additionally, the method would assist the interviewer clarify any misunderstanding with the respondent.
- The researcher could have used simple random sampling so select his sample since he/she is only interested in two variables TV and debt. This method would be preferred since it is simple, less time consuming and ensures that every member of the population is equally likely to be included. However, if the sociologist was interested on how other factors such gender, age, and education level affect TV hours and consequently the debt, then he would consider using stratified random sampling where every element of the population would be grouped into strata and random sampling done on each strata.
- If the researcher was using simple random sampling, the only variables that he would use would be the TV hours per week and the debt the consumer of the TV incurs as a result of being on TV during the hours. However, if chose stratified random sampling additional variables such as age, gender, education level would be included is the survey.
- TV hours and the debt incurred are numerical variables. On the other hand, and if used, gender and education level would be categorical variables while age would be numerical variable.
- The sociologist is likely to face the issues of low response rate in the case he uses telephone administered survey and limitation to people with only mobile numbers, if he uses personal interview, he may find it difficult to reach the respondent, poor recording of data and financial problems if travelling was involved. During data analysis, he is likely to be faced with the problem of sampling error especially if he chose a small sample compared to the population under study.
- The researcher could have decided on the classes of ten based on the largest and the smallest values in his sample and the decided interval range for each class rounded off to the nearest tens (Linoff, 2008). The formula for the number of the class intervals is given by:
For example, in the case of the TV hours it would be:
- The histogram for the two variables are drawn from their respective frequency distributions. The frequency distribution for the TV hours per week is as shown below:
The histogram for the TV hours per week is as shown below:
The frequency distribution for the debt incurred as a result of being active on TV is as shown below:
The histogram for the debt incurred as a result of being on TV is as shown below:
- The numerical summary output results for the two variables based on the researcher’s survey are as shown below:
The mode for debt is #N/A since there is no a most occurring dept.
- Based on the histogram and the numerical summary, the two distributions are a little positively skewed meaning that the number of hours TV is on and the debt incurred is a little above average respectively. Debt is more positively skewed than TV hours. In positive skewness, the mean is the largest, followed by median, then the mode as in television case, though the extent of skewness is very small and can be assumed to concluded that the sample is normally distributed. For better visualization of skewness, the numerical measure of skewness is used and it indicates there is a small degree of positive skew in both cases.
- Since the sociologist is interested in knowing hours on TV lead to debt, the independent variable could be the TV hours while the dependent variable could be the debt incurred as a result of being on TV.
- In excel, the correlation coefficient provides information about the direction and strength of the linear relationship and is determined using the “CORREL” command. It is as follows:
From the value above, the is a little above average positive linear relationship between TV hours and the debt incurred.
- The appropriate plot, to investigate the relationship between Total debt and the TV hours is the scatter plot and its as shown below:
- The regression summary table is as shown below:
The complete table is as shown in the excel sheet. The least square regression equation will be given by:
Where Y is the dependent variable (debt incurred) while the x is the independent variable (TV hours). The intercept of the equation is 49430.02 and indicates the value of debt incurred (dependent variable) when the value of TV hours (independent variable) is zero. The slope is 2531.86 and indicates the degree with which TV hours affect the debt incurred.
- The coefficient of determination R-squared is 0.3066 and it indicates the probability that future outcomes may fall within this predicted range.
- Hypothesis to determine whether there is a linear relationship between the variables. The null hypothesis is that there is no linear relationship while the alternative hypothesis is that there is a linear relationship.
The test statistic is given by:
The p-value for the test statistic from the student t-distribution having n-2 (398) degrees of freedom is P (T≤13.27) =1.0000. The p-value is greater than the significance level of 0.05 hence we reject the null hypothesis in favor of the alternative hypothesis since there is sufficient evidence of a linear relationship between TV hours and the debt incurred as a result of being exposed to TV (Rumsey, 2007).
200-word summary report on the findings of the study conducted by the researcher.
Report
A sociologist believes that people who watch television have a greater exposure to commercials which lead them to buying the goods and hence result to an increasing debt. To justify his claim, he carried a survey on a sample of 400 individuals to determine the number of hours they spend on TV in a week and the debt they incurred as a result of being on TV for those hours.
The result of the study indicate that the average number of hours spent on TV are 30 hours while the average debt incurred from being on TV is $126588.500. The highest number of hours spent on TV in a week is 57hrs while the lowest number of hours spend on TV is 6. On the other hand, the highest debt incurred is $277234.00 while the lowest debt incurred is $20516.00. The research further indicates that the distribution of debt and the number of hours spent on TV is a little bit positively skewed indicating that the greatest percentage of individuals spend a little more than the average hours on TV and incur a little more than average debt for the same. Additionally, hypothesis conducted on the data obtained from the survey indicate that there is a positive linear relationship between the number of hours spent of TV and the debt incurred as a result of exposure to commercials.
References
Linoff, G. (2008). Data analysis using SQL and Excel. Indianapolis, Ind.: Wiley Pub.
Rumsey, D. (2007). Intermediate statistics for dummies. 1st ed. Hoboken, N.J.: Wiley.
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