Confidence Interval Statistics for Business

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

SD

M.E

Lower bound

Upper bound

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 that it 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:

Hypothesized Mean

X-bar

n

Statistical significance

Alpha, a=0.01

Test statistic;

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

= -5.01/1.5498 = -3.2327

Tcritical= 1.645

From the results presented above, the bill in 2019 had a lower mean ($26) than in 2020 ($31.04). 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 bill fall within the confidence interval, indicating that the confidence interval is larger. Also, smaller sample size or a higher variability will lead to a wider confidence interval with a larger margin of error. The level of confidence also affects the interval width. Therefore, my conclusion is reliable because my population bill distribution falls within the confidence interval (Taylor and Cihon, 2004).

(c) Hypothesis Test

Null Hypothesis Ho: µ ? 5

Alternative Hypothesis Ha: µ> 5

The significance level will be ? = 0.1, and a confidence interval is 90%.

Table 3: t Test

Hypothesized Mean

X-bar

n

Statistical significance

T critical

Z obs

Table 3 above presents the t-test results. The results show that since the Zobs > 1.28, we Reject the Ho. Thus, the conclusion arrives that the average monthly electricity bill in a household during the Covid-19 pandemic is $5 greater than that before the Covid-19 pandemic.

(d) Criticize the analysis used by Mr. Tan by identifying three (3) statistical concerns.

I would criticize the analysis conducted by Mr. Tan by identifying three (3) statistical concerns. One major statistical concern relating to Mr. Tan's analysis is committing an error of measurement, evident from the provided data values. The mean electricity bill in 2019 was $26, and that of May 2020 was $31.04. Their standard deviations were the 2019 bill ($7), and 2020 was $31.04. We can see a slight difference in the electricity bill consumption. He hypothesized that the average monthly electricity bill during the Covid-19 pandemic was $5 greater than before the Covid-19 pandemic, but this was not the case. After computations, I found that the means increased by $5.04. Thus, I will make sure these errors are minimal to avoid misinterpretation of the data sets.

Another major concern that may arise from Mr. Tan's analysis is that data entry errors were caused by incorrect entry of the values of bills, which may have triggered the increase in the electricity bill in May 2020. Thus, to correct this error, I will double-check the data collected and enter the same in excel.

The last major concern emanates from the analysis by comparing 2019 and 2020. Mr. Tan provided the data sets for the bill of 2020 only. Instead, he should have provided for both 2019 and 2020. Therefore, I will address the above mentioned by collecting the data sets for the two years, 2019 and 2020, concerning the electricity consumption and covid 19 cases. I use the independent t-test to compare the electricity bill between the two years.

(257 words)

(e) 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 that it 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 a significant increase in electricity bills by $5.04.