Data Set 8-4 :A random sample of 64 students produced the following statistics: = 18.00, = 7.00.
-The 99 percent confidence interval about the mean in Data Set 8-4 is
A) -0.69 to 36.69
B) 17.71 to 18.29
C) 15.67 to 20.33

Question

Quizplus · Accepted Answer

The 99% confidence interval for the mean is calculated using the formula: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. Given $\bar{x} = 18.00$, $\sigma = 7.00$, and $n = 64$, and knowing that the z-score for a 99% confidence level is approximately 2.576, the calculation is $18 \pm 2.576\frac{7}{\sqrt{64}}$, which simplifies to $18 \pm 2.576 \times \frac{7}{8}$, resulting in the interval $15.67$ to $20.33$.

Data Set 8-4 :A Random Sample of 64 Students Produced