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 ______________.
A)19,232 to 20,768
B)19,365 to 20,635
C)19,229 to 20,771
D)19,367 to 20,633
E)119.89 to 122.1218,500 to 21,500

Question

Quizplus · Accepted Answer

We can use the formula for the confidence interval of a population mean:
CI = x̄ ± t*(s/√n)
where x̄ is the sample mean (20,000), s is the sample standard deviation (1,500), n is the sample size (17), and t is the critical value from the t-distribution with degrees of freedom (df) = n-1 and confidence level = 95%. From a t-distribution table with df = 16 and confidence level = 95%, we find t = 2.131. Substituting these values, we get:
CI = 20,000 ± 2.131*(1,500/√17) = (19,229, 20,771)
Therefore, the 95% confidence interval for the population mean weight of a semi tracker truck is (19,229 to 20,771), which is closest to choice C.

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