Ramdom sample of 41 car owners results in a mean of 7 years. Population standard deviation of 3.75 years. Find a 95% confidence interval for the true population mean..My answer is
(5.9, 8.1) but having problems with margin of error
To find the 95% confidence interval for the true population mean, we can use the formula:
Confidence Interval = sample mean ± (Z-score * (population standard deviation / √sample size))
First, let's find the Z-score for a 95% confidence level. The Z-score corresponding to a 95% confidence level can be found using a standard normal distribution table or a calculator. The Z-score for a 95% confidence level is approximately 1.96.
Next, plug the values into the formula:
Confidence Interval = 7 ± (1.96 * (3.75 / √41))
Now, let's calculate the margin of error:
Margin of Error = 1.96 * (3.75 / √41)
The sample mean is 7 years, so the lower bound of the confidence interval is:
Lower Bound = 7 - (1.96 * (3.75 / √41))
And the upper bound is:
Upper Bound = 7 + (1.96 * (3.75 / √41))
Calculate the margin of error:
Margin of Error = 1.96 * (3.75 / √41) ≈ 1.221
Now, let's calculate the lower bound:
Lower Bound = 7 - 1.221 ≈ 5.779
And the upper bound:
Upper Bound = 7 + 1.221 ≈ 8.221
Therefore, the 95% confidence interval for the true population mean is approximately (5.779, 8.221). Hence, your answer of (5.9, 8.1) is almost correct, but slightly off due to rounding errors.