An environmental group at a local college is conducting independent tests to determine the distance a particular make of automobile will travel while consuming only 1 gallon of gas.A sample of five cars is tested and a mean of 28.2 miles is obtained.Assuming that the standard deviation is 2.7 miles,find the 95% confidence interval for the mean distance traveled by all such cars using 1 gallon of gas.
A)[26.16 30.24]
B)[20.70 35.70]
C)[24.85 31.55]
D)[26.70 29.70]
E)[25.83 30.57]

Question

Quizplus · Accepted Answer

To find the 95% confidence interval, we use the formula:

CI = x̄ ± tα/2 * (S/√n)

where x̄ = sample mean, S = sample standard deviation, n = sample size, and tα/2 = t-value for the desired confidence level and degrees of freedom (df = n-1).

For 95% confidence level and df = 4, tα/2 = 2.776.

Plugging in the values, we get:

CI = 28.2 ± 2.776 * (2.7/√5)
   = [24.84, 31.56]

Rounding to two decimal places, the answer is [24.85, 31.55]. Therefore, the best choice is C.

An Environmental Group at a Local College Is Conducting Independent