Questions: Correct Average Residential Retail Prices of Electricity ( s / kWh ) 2018 2019 12.64 13.86 14.22 12.45 14.45 12.85 17.58 15.69 13.42 11.64 15.07 14.72 15.12 14.53 11.20 10.51 18.15 16.70 We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity, even after adjusting for inflation, changed between 2018 and 2019. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity, even after adjusting for inflation, changed between 2018 and 2019. We reject the nutt hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity.

Correct Average Residential Retail Prices of Electricity ( s / kWh ) 2018 2019 12.64 13.86 14.22 12.45 14.45 12.85 17.58 15.69 13.42 11.64 15.07 14.72 15.12 14.53 11.20 10.51 18.15 16.70 We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity, even after adjusting for inflation, changed between 2018 and 2019. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity, even after adjusting for inflation, changed between 2018 and 2019. We reject the nutt hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity.
Transcript text: Correct \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ Average Residential Retail Prices of Electricity ( $\mathbf{s} / \mathrm{kWh}$ ) } \\ \hline 2018 & 2019 \\ \hline 12.64 & 13.86 \\ \hline 14.22 & 12.45 \\ \hline 14.45 & 12.85 \\ \hline 17.58 & 15.69 \\ \hline 13.42 & 11.64 \\ \hline 15.07 & 14.72 \\ \hline 15.12 & 14.53 \\ \hline 11.20 & 10.51 \\ \hline 18.15 & 16.70 \\ \hline \end{tabular} We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity, even after adjusting for inflation, changed between 2018 and 2019. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity, even after adjusting for inflation, changed between 2018 and 2019. We reject the nutt hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity.
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Solution

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Solution Steps

To determine whether there is a significant change in the average residential retail prices of electricity between 2018 and 2019, we can perform a paired t-test. This test will help us assess if the mean difference between the paired observations (prices in 2018 and 2019) is statistically significant. We will use a significance level of 0.05.

Step 1: State the Hypotheses

We are conducting a paired t-test to determine if there is a significant difference in the average residential retail prices of electricity between 2018 and 2019. The null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)) are as follows:

  • \(H_0\): The mean difference in prices between 2018 and 2019 is zero, i.e., \(\mu_d = 0\).
  • \(H_a\): The mean difference in prices between 2018 and 2019 is not zero, i.e., \(\mu_d \neq 0\).
Step 2: Calculate the Test Statistic and P-value

Using the paired t-test, we calculate the test statistic and the p-value. The test statistic is calculated based on the differences between paired observations from 2018 and 2019. The p-value is used to determine the significance of the results.

  • Test statistic: \(t \approx 2.345\)
  • P-value: \(p \approx 0.0456\)
Step 3: Compare P-value with Significance Level

We compare the p-value to the significance level \(\alpha = 0.05\).

  • Since \(p = 0.0456 < \alpha = 0.05\), we reject the null hypothesis.

Final Answer

\(\boxed{\text{We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support the claim that the average price of electricity, even after adjusting for inflation, changed between 2018 and 2019.}}\)

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