Statistics Assignment: Level of Measurement and Central Tendency

Question 1 (26 marks)

a) 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.

1. Time on email – How many hours per week do you spend sending and answering email?

2. Life satisfaction – On the whole, are you very satisfied, fairly satisfied, not very satisfied, or not at all satisfied with the life you lead?

3. Monthly income – What is your monthly income in SGD?

4. Attitude toward death penalty – Do you favour or oppose the death penalty for personsconvicted of murder?

5. Marital status – Are you currently married, widowed, divorced, separated, or have you never been married? (5 marks)

b) 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 (3marks)?

c) 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.

Question 2 (14 marks)

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 necessary calculations. Interpret the hypothesis testing results (use = 0.01) and report your conclusion

Question 3 (30 marks)

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 neighbours. The following table shows the frequency distribution of respondents of various age categories who mentioned or did not mention homosexuals

a) Formulate the null and research hypotheses for testing whether the relationship between age category and attitude toward having homosexuals as neighbours holds in the population of adult citizens in Singapore. (5 marks)

b) Construct a table containing the expected frequencies