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?Luhmann, Schimmack, and Eid (2011) were interested in the relationship between income
Chapter 4, Problem 33(choose chapter or problem)
Luhmann, Schimmack, and Eid (2011) were interested in the relationship between income and subjective well-being. The researchers measured participants’ income across time between 1991 and 2006 and observed that both the central tendency and variability of income tended to increase across time. The following annual income scores (in thousands of dollars) are similar to the data observed by Luhmann et al.
\(\begin{array}{rc} \hline 1991 & 2006 \\ \hline 8 & 15 \\ 18 & 13 \\ 3 & 11 \\ 8 & 27 \\ 8 & 5 \\ 3 & 21 \\ 13 & 3 \\ 3 & 23 \\ 8 & 17 \\ \hline \end{array}\)
a. Compute \(M, S S, s^{2}\), and s for these samples.
b. Report these descriptive statistics in a format that is appropriate for a scientific journal.
Questions & Answers
QUESTION:
Luhmann, Schimmack, and Eid (2011) were interested in the relationship between income and subjective well-being. The researchers measured participants’ income across time between 1991 and 2006 and observed that both the central tendency and variability of income tended to increase across time. The following annual income scores (in thousands of dollars) are similar to the data observed by Luhmann et al.
\(\begin{array}{rc} \hline 1991 & 2006 \\ \hline 8 & 15 \\ 18 & 13 \\ 3 & 11 \\ 8 & 27 \\ 8 & 5 \\ 3 & 21 \\ 13 & 3 \\ 3 & 23 \\ 8 & 17 \\ \hline \end{array}\)
a. Compute \(M, S S, s^{2}\), and s for these samples.
b. Report these descriptive statistics in a format that is appropriate for a scientific journal.
ANSWER:Step 1 of 4
We have to find \(M, S S, s^{2}\) and s for these samples. Assume 1991 year be x and 2006 year be y.
\(M \rightarrow \text { Mean }\)
\(s s \Rightarrow \sum(x-\bar{x})^{2} \rightarrow\) sum of square
\(s^{2} \Rightarrow \sum \frac{(x-\bar{x})^{2}}{N} \rightarrow\) variance
\(s \rightarrow \sqrt{s} \rightarrow\) standard deviation