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____________.

Accepted Solution

Answer:(19229.11 ,20770.89)Step-by-step explanation:We are given the following information:Sample size, n = 17Sample mean = 20,000 pounds Sample standard deviation = 1,500 poundsConfidence level = 95%Significance level = 5% = 0.05 95% Confidence interval:  [tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]  Putting the values, we get,  [tex]t_{critical}\text{ at degree of freedom 16 and}~\alpha_{0.05} = \pm 2.119[/tex]  [tex]20000 \pm 2.119(\displaystyle\frac{1500}{\sqrt{17}} ) = 20000 \pm 770.89 = (19229.11 ,20770.89)[/tex]