During the Covid-19 pandemic, working from home has become the norm. Because of this, many households face an increasing monthly electricity bill.
Mr. Tan is a research student at the Singapore University of Social Sciences, and his research focus is to examine the impact of Covid-19 on household electricity consumption. He hypothesised that the average monthly electricity bill in a household has increased more than $5 during the Covid-19 pandemic. In order to test his hypothesis, he collected the electricity bill data in 50 households in May 2020 when Singapore was during the circuit breaker period.
Mr. Tan also found that the mean and standard deviation of electricity bill in a household in May 2019 are $26 and $7, respectively.
In order to study the impact of Covid-19 on household electricity consumption, Mr. Tan intends to make a comparison of the average electricity bills in May 2019 and May 2020 in his analysis.
The data is given in the Excel data file.
Question 1
(a) Using relevant Excel reports, state the values of three (3) location measures and three (3) dispersion measures of electricity bill in a household in May 2020.
(12 marks)
(b) Assume that the electricity bill in a household in May 2019 follows a normal distribution, what is the probability that a randomly selected household had an electricity bill greater than $31 in May 2019? Please use two methods (i.e., Z-table manual method, and the Excel function) to solve it, and round your answer to four decimal places.
(18 marks)
(c) Describe the interquartile range, and explain which one is more appropriate to measure dispersion – standard deviation or interquartile range?
(30 marks)
(d) Using appropriate charts and numerical measures, develop a summary report to address Mr Tan’s hypothesis. You are expected to provide interpretation to the charts and numerical measures. You are not required to do any further inferential analysis. The word limit is 300 words. Please indicate the word count at the end of your answer.
(40 marks)
