Question

"In a random sample of 20 people, the mean commute time to work was 34.3 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a t-distribution to construct a 95% confidence interval for the population mean commute time."

Answer 1

We can be 95% confident that the true population mean commute time lies between 30.88 and 37.72 minutes.

Step-by-step explanation:

95% Confidence Interval for Population Mean Commute Time

Given:

• Sample size (n) = 20
• Sample mean (x) = 34.3 minutes
• Sample standard deviation (s) = 7.3 minutes
• Confidence level = 95%

Steps:

1. Find the degrees of freedom (df).

df = n - 1

df = 20 - 1

df = 19

2. Find the t-value for the desired confidence level and degrees of freedom.

Using a t-table or calculator, we find t ≈ 2.093

3. Calculate the margin of error (E)

E = t * s / √n

E ≈ 2.093 * 7.3 / √20

E ≈ 3.41 minutes

4. Calculate the confidence interval.

Lower bound = x - E

Upper bound = x + E

Lower bound = 34.3 - 3.41 ≈ 30.88 minutes

Upper bound = 34.3 + 3.41 ≈ 37.72 minutes