Question

the u.s. energy information administration claimed that u.s. residential customers used an average of 10,219 kilowatt hours (kwh) of electricity this year. a local power company believes that residents in their area use more electricity on average than eia's reported average. to test their claim, the company chooses a random sample of 122 of their customers and calculates that these customers used an average of 10,458kwh of electricity last year. assuming that the population standard deviation is 1485kwh , is there sufficient evidence to support the power company's claim at the 0.02 level of significance?

Answer 1

Main answer

Based on the given data, we do not have enough evidence to support the power company's claim that the average electricity usage in their area is greater than the EIA's reported average at the 0.02 level of significance.

Explanation:

To determine if there is sufficient evidence to support the power company's claim at the 0.02 level of significance, perform a hypothesis test using the given information.

Let's define the hypotheses:

Null Hypothesis (H0): The average electricity usage in the local power company's area is the same as the EIA's reported average.

Alternative Hypothesis (Ha): The average electricity usage in the local power company's area is greater than the EIA's reported average.

Set up the hypotheses as follows:

H0: μ = 10,219 (population mean)

Ha: μ > 10,219 (population mean)

Given:

Sample size (n) = 122

Sample mean (x) = 10,458

Population standard deviation (σ) = 1485

To test the claim, perform a one-sample t-test.

The test statistic can be calculated using the formula:

t = (x - μ) / (σ / √n)

Substituting the provided values:

t = (10,458 - 10,219) / (1485 / √122)

t = 239 / (1485 / √122)

t ≈ 239 / 133.56

t ≈ 1.78

To determine the critical value at the 0.02 level of significance, we need to find the corresponding t-value from the t-distribution table or calculator with (n - 1) degrees of freedom.

Since the sample size is 122, the degrees of freedom (df) = 122 - 1 = 121.

Looking up the critical t-value for a one-tailed test with a significance level of 0.02 and 121 degrees of freedom, we find the critical t-value to be approximately 2.364.

Since our calculated t-value (1.78) is less than the critical t-value (2.364), we fail to reject the null hypothesis.

Therefore, based on the given data, we do not have enough evidence to support the power company's claim that the average electricity usage in their area is greater than the EIA's reported average at the 0.02 level of significance.