7. Sampling Distributions & Confidence Intervals: Mean
Confidence Intervals for Population Mean
Struggling with Statistics for Business?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
You want to purchase one of the new Altima. You randomly select 400 dealerships across the United States and find a mean of $25,000. Assume a population standard deviation of $2500. Construct and interpret a 94% confidence interval for the true mean price for the new Nissan Altima.
A
(24992.5, 25007.5); We are 94% confident that the true mean price for the new Nissan Altima falls between $24992.5 and $25007.5.
B
(24882.438, 25117.563); We are 94% confident that the true mean price for the new Nissan Altima falls between $24882.438 and $25117.563.
C
(24764.875, 25235.15); We are 94% confident that the true mean price for the new Nissan Altima falls between $24764.875 and $25235.15.
D
(24529.75, 25470.25); We are 94% confident that the true mean price for the new Nissan Altima falls between $24529.75 and $25470.25.
Verified step by step guidance1
Identify the given values: sample mean (\(\bar{x}\)) is $25,000, population standard deviation (\(\sigma\)) is $2,500, sample size (\(n\)) is 400, and the confidence level is 94%.
Determine the z-score corresponding to a 94% confidence level. Since the confidence level is 94%, the remaining 6% is split equally in the two tails of the normal distribution. Look up the z-score for 3% in a standard normal distribution table or use a calculator to find it.
Calculate the standard error of the mean (SE) using the formula: \(SE = \frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.
Compute the margin of error (ME) using the formula: \(ME = z \times SE\), where \(z\) is the z-score found in step 2 and \(SE\) is the standard error calculated in step 3.
Construct the confidence interval using the formula: \(\bar{x} \pm ME\), where \(\bar{x}\) is the sample mean and \(ME\) is the margin of error. This will give you the lower and upper bounds of the confidence interval.
4:48mWatch next
Master Population Standard Deviation Known with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
