A researcher is interested in estimating the mean weight of a semi tractor 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 90% confidence interval for the population mean weight of a semi tractor truck is ______________.
A)19,365 to 20,635
B)19,367 to 20,633
C)19,514 to 20,486
D)19,515 to 20,485
E)18,500 to 21,500

Question

Quizplus · Accepted Answer

The 90% confidence interval for the population mean can be calculated using the formula: $\bar{x} \pm t_{\alpha/2} \times \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $t_{\alpha/2}$ is the t-score for the desired confidence level with $n-1$ degrees of freedom. Given $\bar{x} = 20,000$, $s = 1,500$, $n = 17$, and for a 90% confidence interval with 16 degrees of freedom, the t-score is approximately 1.746. Plugging these values into the formula gives a confidence interval of approximately 19,365 to 20,635.

A Researcher Is Interested in Estimating the Mean Weight of a Semi