STATISTICS FOR BUSINESS & ECONOMICS

Statistics for Business & Economics

Question 1

(a) Describe the 90% confidence interval for the average electricity bill in a household in May 2020. Interpret the meaning of the 90% confidence.

Table 1: 90% CI for the Electricity Bill

90% CI for Bill (2020)

Mean

31.036

SD

8.431446

M.E

1.999097

Lower bound

29.0369

Upper bound

33.0351

Table 1 above presents the 90% confidence interval for the electricity bill. The results show that the 90% confidence interval was (29.04, 33.04). The 90% CI implies that the population means of bill fall within the confidence interval, indicating that the population means were significant at 10%. Hence, we can say thatit is likely that the population means the true value.

Discuss whether he can conclude that the average monthly electricity bill during the Covid-19 pandemic is $5 greater than that before the Covid-19.

In addressing this question, I will use the independent t-test. This inferential statistical test aims to compare the means of the two groups independent of each other and assess if there is statistical evidence that the associated means of the population differs significantly (Weaver, Morales, and Dunn, 2017). Thus, I will aim to evaluate if the mean differences in electricity consumption between 2019 and 2020 differ significantly. The following hypothesis was proposed to aid in guiding my study;

Ho: No significant mean differences of the electricity bill for 2019 and 2020

Ha: There is a significant mean difference in the electricity bill for 2019 and 2020

Hypothesis Testing

Table 2:

2019

2020

Hypothesized Mean

X-bar

26

31.04

?

7

8.4314

n

50

50

Statistical significance

?

0.1

Alpha, a=0.01

Test statistic;

T= (26-31.04)/ sqrt [(72/50+8.43142/50)]

= -5.01/1.5498 = -3.2327

Tcritical=...

The t-test results were presented as t=-3.23< 1.645. We reject the Ho, and the conclusion has arrived that the average monthly electricity bill in a household during the Covid-19 pandemic is $5 greater than before the Covid-19.

(b) Discussion on effect of the confidence interval and sample size

In addressing this question, the conclusion will change if the 99.99% confidence interval is used and the number of data is a quarter of the original data set (a smaller sample size); this is because as we increase the confidence level, the width of the confidence interval also increases. Thus, a larger confidence level increases the chance that the population means of...

…Summarize the above analysis in a simplified report for Mr. Tan.

The current study aimed to compare the impacts of the covid 19 on the electricity consumption for the May 2019 and May 2020 periods. The study applied the independent t-test, which aims to compare the electricity consumption for two years. The study found that the 90% confidence interval was (29.04, 33.04). The 90% CI implies that the population means of bill fall within the confidence interval, indicating that the population means were significant at 10%. Hence, one could point out that thatit is likely that the population means the true value (Myers, Well, and Lorch, 2010). Also, there were significant mean differences in electricity bills between 2019 and 2020. The conclusion arrived at indicates that the average monthly electricity bill in a household during the Covid-19 pandemic is $5 greater than before the Covid-19 at 10%. Also, the change in the confidence interval to 99.99% and smaller sample size will lead to a wider confidence interval with a larger margin of error (Sheskin, 2010). The level of confidence also affects the interval width. Therefore, my conclusion was…