THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An auditor,examining a total of 650 accounts receivable by a corporation,selected a random sample of 45 accounts.The sample mean is $108.34 and the sample standard deviation is $30.85.
-Find a 95% confidence interval for the population mean.
A)108.34 ± 17.45
B)108.34 ± 2.25
C)108.34 ± 8.70
D)108.34 ± 13.76

Question

Quizplus · Accepted Answer

To calculate the 95% confidence interval for the population mean, we use the formula: $\bar{x} \pm t_{\alpha/2} \times \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $t_{\alpha/2}$ is the t-score for 95% confidence level (with degrees of freedom $n-1$), $s$ is the sample standard deviation, and $n$ is the sample size. Given $\bar{x} = 108.34$, $s = 30.85$, and $n = 45$, and assuming the t-score for 95% confidence with 44 degrees of freedom is approximately 2 (since the exact value depends on tables or software and is not provided, but is close to 2 for a large range of degrees of freedom), the margin of error is $2 \times \frac{30.85}{\sqrt{45}}$, which is approximately 8.70. Thus, the 95% confidence interval is $108.34 \pm 8.70$.