SOC392: Methods of Data Analysis: Exploring Behavioural Sciences Question 1 1. For the following five variables, identify the level at which it is measured (nominal, ordinal, interval, or ratio) and then whether it is a discrete or continuous variable. Time on email – How many hours per week do you spend sending and answering emails? Life satisfaction – On the whole, are you very satisfied, fairly satisfied, not very satisfied, or not at all satisfied with the life you lead?

Question 1
1. For the following five variables, identify the level at which it is measured (nominal, ordinal, interval, or ratio) and then whether it is a discrete or continuous variable.
Time on email – How many hours per week do you spend sending and answering emails? Life satisfaction – On the whole, are you very satisfied, fairly satisfied, not very satisfied, or not at all satisfied with the life you lead?
Monthly income – What is your monthly income in SGD?
Attitude toward the death penalty – Do you favor or oppose the death penalty for persons convicted of murder?
Marital status – Are you currently married, widowed, divorced, separated, or have you never been married?
2. Based on the following frequency distribution histogram for a set of 14 scores, analyse the shape of the distribution and justify your answer (3 marks). Describe the positions of the mode, median, and mean in the distribution (3 marks). Which of the three measures of central tendency would you recommend to use, and why?

3. According to a 2016 study in Singapore, 12-year-olds spend 6.5 hours on electronic devices each day. Assuming that the distribution of screen time is normal with a standard deviation of = 2 hours, find each of the following proportions. You may apply the formulae below and may also find the unit normal table in your textbook helpful. z = (Χ-μ)/σ.
What proportion of 12-year-old children spend more than 8 hours on electronic devices each day?
What proportion of 12-year-old children spend less than 30 minutes a day on electronic devices?
Question 2 
A researcher wanted to know whether the average age at first marriage was higher for all married males versus all married females in Singapore. The means and standard deviations for a random sample of 392 married men and 610 married women (randomly selected from among all married adults in Singapore) are presented in the table below. Formulate the null and research hypotheses. Calculate the t-statistic, showing all the necessary calculations. Interpret the hypothesis testing results (use a = 0.01) and report your conclusion.

Question 3
In the World Values Survey Wave 6 carried out by the Centre for Applied Research, SIM University in Singapore in 2012, a nationally representative sample of Singapore citizens aged 18 years or older were given a list of various groups of people. They were then asked to mention any group that they would not like to have as neighbors. The following table shows the frequency distribution of respondents of various age categories who mentioned or did not mention homosexuals.

1. Formulate the null and research hypotheses for testing whether the relationship between age category and attitude toward having homosexuals as neighbors holds in the population of adult citizens in Singapore.
2. Construct a table containing the expected frequencies ( ).
3. Compute the chi-square statistic.You may apply the following formulae to help you answer the question. χ² = Σ (f0-fe)²/fe.
4. Calculate the degrees of freedom for the table.
5. Determine the p-value for the chi-square statistic
6. Analyze whether there is evidence to reject the null hypothesis (use α = 0.01). Justify your decision.
7. To measure the effect size, which of the two measures (the phi-coefficient or Cramér’s ) should you use, and why? Use your chosen measure and report the effect size. You may use any of the following formulae below to help you answer this question. Φ=√χ²/n V=√χ²/n(df∗) 𝑁𝑜𝑡𝑒: 𝑑𝑓∗ 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑚𝑎𝑙𝑙𝑒𝑟 𝑜𝑓 𝑒𝑖𝑡ℎ𝑒𝑟 (𝑅 − 1) 𝑜𝑟 (𝐶 − 1)
8. Interpret the results of the hypothesis test in terms of the relationship between age category and attitude toward having homosexuals as neighbors among adult citizens in Singapore.

Question 4
Researcher K wants to understand if there is a correlation between GDP per capita and life expectancy at birth. She obtained data on these two variables as in the year 2017 for 233 countries from the World Bank.
1. First, she calculated the coefficient of correlation (Pearson’s r) and found the correlation to be 0.667. Interpret what this means. Next, calculate the coefficient of determination and discuss its meaning.
2. Researcher K wishes to develop a linear equation to express the relationship between the two variables. She let GDP per capita by the independent variable and life expectancy at birth be the dependent variable. She then conducted regression analysis in Excel and the results are shown below.

Based on these results, write the regression equation for predicting life expectancy at birth (years) from GDP per capita (current US$).
For a country with a GDP per capita of US$ 60,000, estimate the life expectancy at birth.
Analyse the regression results.
3. Below is a scatter plot showing the data points K used in her study.

Examine the scatter plot and discuss whether the relationship between GDP per capita and life expectancy at birth is truly linear.
If the researcher restricts data points to the area within box A, how will the coefficient of correlation between GDP per capita and life expectancy at birth change? How will she then conclude about the relationship between the two?
If the researcher restricts data points to the area within box B, how will the coefficient of correlation between GDP per capita and life expectancy at birth change? How will she then conclude about the relationship between the two