Question

a random sample of 160 households is selected to estimate the mean amount spent on electric service. a 95% confidence interval was determined from the sample results to be ($151, $216). which of the following is the correct interpretation of this interval? a. we are 95% confident that the mean amount spent on electric service among all households is between $151 and $216. b. 95% of the households will have an electric bill between $151 and $216. c. we are 95% confident that the mean amount spent on electric service among the 160 households is between $151 and $216. d. there is a 95% chance that the mean amount spent on electric service is between $151 and $216. question 5 a survey of a random sample of 1,500 young americans found that 87% had earned their high school diploma. based on these results, the 95% confidence interval for the proportion of young americans who have earned their high school diploma is (0.853,0.887) what is the margin of error for this confidence interval? a. 0.95

Explanation:

Step1: Recall confidence - interval concept

A confidence interval for the population mean gives a range of values within which we are a certain percentage (confidence level) confident that the true population mean lies.

Step2: Analyze Question 4 options

For a 95% confidence interval for the mean amount spent on electric service, it means we are 95% confident that the mean amount spent on electric service among all households (the population) is between the given interval values. Option A is correct as it refers to the population mean. Option B is wrong as it refers to individual households' bills instead of the population mean. Option C refers to the sample mean of the 160 households, but the confidence - interval is for the population mean. Option D misinterprets the confidence level as a probability for the mean to be in the interval.

Step3: Recall margin - of - error formula for proportion

The formula for a confidence interval for a proportion $p$ is $\hat{p}\pm E$, where $\hat{p}$ is the sample proportion and $E$ is the margin of error. If the confidence interval is $(L, U)$ (lower and upper limits), then $E=\frac{U - L}{2}$.

Step4: Calculate margin of error for Question 5

Given the confidence interval for the proportion of young Americans who have earned their high - school diploma is $(0.853,0.887)$. The margin of error $E=\frac{0.887 - 0.853}{2}=\frac{0.034}{2}=0.017$.

Answer:

Question 4: A. We are 95% confident that the mean amount spent on electric service among all households is between $151 and $216.
Question 5: The margin of error is 0.017.