Question

A researcher is interested in estimating the mean weight of a semi tracker truck to determine the potential load capacity. She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500. The 95% confidence interval for the population mean weight of a semi tracker truck is____________.

Answer 1

(19229.11 ,20770.89)

Explanation:

We are given the following information:

Sample size, n = 17

Sample mean = 20,000 pounds

Sample standard deviation = 1,500 pounds

Confidence level = 95%

Significance level = 5% = 0.05

95% Confidence interval:

`\bar{x} \pm t_(critical)\displaystyle(s)/(√(n))`

Putting the values, we get,

`t_(critical)\text{ at degree of freedom 16 and}~\alpha_(0.05) = \pm 2.119`

`20000 \pm 2.119(\displaystyle(1500)/(√(17)) ) = 20000 \pm 770.89 = (19229.11 ,20770.89)`