Asked by Cassidy Hoeckendorf on Jun 10, 2024
Verified
In order to estimate the average electric usage per month, a sample of 64 houses was selected and the electric usage was determined.Assume a population standard deviation of 320 kilowatt-hours.If the sample mean is 1858 kWh, the 95% confidence interval estimate of the population mean is _____ kWh.
A) 1779.6 to 1936.4
B) 1818 to 1898
C) 1792.2 to 1923.8
D) 1538 to 2178
Confidence interval estimate
A range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter, given a specified level of confidence.
Standard deviation
A measure of the amount of variation or dispersion of a set of values, indicating how spread out the values in a data set are.
Electric usage
The amount of electrical energy consumed by a residence, industry, or equipment in a specific period.
- Comprehend and determine confidence intervals for population means and proportions.
Verified Answer
KS
Karen SerranoJun 14, 2024
Final Answer :
A
Explanation :
The 95% confidence interval for the population mean is calculated using the formula: xˉ±Zσn\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}xˉ±Znσ , where xˉ\bar{x}xˉ is the sample mean, ZZZ is the Z-score corresponding to the confidence level (for 95%, Z=1.96Z = 1.96Z=1.96 ), σ\sigmaσ is the population standard deviation, and nnn is the sample size. Plugging in the given values: 1858±1.9632064=1858±1.96×40=1858±78.41858 \pm 1.96 \frac{320}{\sqrt{64}} = 1858 \pm 1.96 \times 40 = 1858 \pm 78.41858±1.9664320=1858±1.96×40=1858±78.4 , which gives the interval 1779.61779.61779.6 to 1936.41936.41936.4 kWh.
Learning Objectives
- Comprehend and determine confidence intervals for population means and proportions.