Question

Given the following data about Renewable electricity output (% of total electricity output) in different countries:

12.442, 80.081, 50.055, 65.326, 39.747, 15.856, 22.679, 29.392, 63.263, 62.198

(a) Construct a 95% confidence interval on the mean renewable electricity output.
i. Calculate the sample mean and variance.
ii. Write the appropriate confidence formula and the assumptions.
iii. Calculate the confidence interval manually.
iv. Perform the analysis by Minitab.

(b) According to the energy industry experts it is believed that the mean renewable electricity output is not more than 22%. Do you think the data supports the claim? Test the hypothesis. Use a significance level of 0.05.
i. State the hypotheses.
ii. Test manually: Compute the test statistic. Find p-value and write your rejection criterion. Make the decision to reject or not reject the null hypothesis. Summarize the results and interpret your decision.
iii. Test the hypotheses by using Minitab.

Answer 1

To construct a 95% confidence interval on the mean renewable electricity output, calculate the sample mean and variance, write the confidence formula and assumptions, calculate the confidence interval manually, and perform the analysis by Minitab. To test the hypothesis that the mean renewable electricity output is not more than 22%, state the hypotheses, compute the test statistic, find the p-value, and make the decision. Perform the hypothesis test using Minitab.

Step-by-step explanation:

To construct a 95% confidence interval on the mean renewable electricity output, we need to follow several steps:

i. Calculate the sample mean and variance. The sample mean is the average of all the data points, and the sample variance is a measure of how spread out the data is. ii. Write the appropriate confidence formula and assumptions. The confidence formula is: Sample mean ± (Critical value) × (Standard deviation of the sample mean). The assumptions are that the data is normally distributed and the sample is random and independent. iii. Calculate the confidence interval manually by substituting the values into the formula. iv. Perform the analysis by Minitab by inputting the data and selecting the appropriate test.

b. To test the hypothesis that the mean renewable electricity output is not more than 22%, we need to state the hypotheses, compute the test statistic, find the p-value, and write the rejection criterion. We then make the decision to either reject or not reject the null hypothesis and interpret the results. Perform the hypothesis test using Minitab by inputting the data and selecting the appropriate test.