Question

A recent study of 25 students showed that they spend an average of $18.35 for gasoline per week. The standard deviation of the sample was $3.00. Construct the 95% confidence interval of the population mean.

What is the:

a) Sample Size (n)
b) Standard Deviation (s)
c) Sample Mean (x-bar)
d) Path

Answer 1

To construct a 95% confidence interval for the population mean, use the formula CI = x-bar ± Z * (s/√n), where n is the sample size, s is the standard deviation, x-bar is the sample mean, and Z is the Z-score. Substituting the given values into the formula, the final confidence interval can be calculated.

Step-by-step explanation:

To construct a 95% confidence interval for the population mean, we can use the formula:

CI = x-bar ± Z * (s/√n)

1. Sample Size (n): The sample size is given as 25.
2. Standard Deviation (s): The standard deviation of the sample is $3.00.
3. Sample Mean (x-bar): The sample mean is $18.35.
4. Path: To find the path, we need to determine the Z-score associated with a 95% confidence level. The Z-score can be obtained from a standard normal distribution table or a calculator, and for a 95% confidence level, the Z-score is approximately 1.96.

Substituting these values into the formula, we have:

CI = 18.35 ± 1.96 * (3/√25)