Please advise-Thank you.
The Center for Urban Transportation research released a report stating that the average commuting distance in the United States is 10.9 miles Suppose that this average is actually the mean of a sample of 300 commuters and that the sample deviation was 6.2 mi. Estimate the true mean commuting distance using a 99% confidence interval.
Formula using 99% confidence interval:
CI99 = mean ± (2.58)(sd/√n)
Note: ± 2.58 represents 99% confidence interval.
mean = 10.9
sd = 6.2
n = 300
Plug the values into the formula and calculate.
I hope this will help get you started.
I worked it out using + 10.9 =11.82352949 and 10.9 (-) =9.9764501 but how do I word my answer? What does this mean?
This is indicating that there is a 99% chance that the population mean is somewhere within this range (9.98-11.82).
Thanks Much!
To estimate the true mean commuting distance using a 99% confidence interval, you can follow the steps below:
Step 1: Determine the sample mean.
In this case, the sample mean is given as 10.9 miles.
Step 2: Calculate the standard error.
The standard error (SE) represents the variability of the sample mean. It is calculated by dividing the sample standard deviation (6.2 mi) by the square root of the sample size (√300). The formula is SE = σ / √n, where σ is the population standard deviation and n is the sample size.
SE = 6.2 / √300
Step 3: Find the critical value.
Since we want to construct a 99% confidence interval, we need to find the critical value associated with a confidence level of 99%. The critical value is obtained from a t-distribution table or a statistical calculator. For this question, the critical value will be approximately 2.626 (assuming a large sample size).
Step 4: Calculate the margin of error.
The margin of error (ME) is calculated by multiplying the critical value by the standard error. The formula is ME = critical value * SE.
ME = 2.626 * (6.2 / √300)
Step 5: Construct the confidence interval.
To construct the confidence interval, subtract and add the margin of error to the sample mean. The formula is:
Confidence Interval = Sample Mean ± Margin of Error
CI = 10.9 ± (2.626 * (6.2 / √300))
Now you can calculate the lower and upper bounds of the confidence interval:
Lower Bound = 10.9 - (2.626 * (6.2 / √300))
Upper Bound = 10.9 + (2.626 * (6.2 / √300))
Calculate the values using a calculator or spreadsheet to find the confidence interval, which will provide an estimate of the true mean commuting distance with 99% confidence.