Confidence Interval Statistics Business Analysis Statistics

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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 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:


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= 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(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,…

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…bill of 2020 only. Instead, he should have provided for both 2019 and 2020.

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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….....

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