statistics range rule of thumb confidence interval
Suppose that the minimum and maximum ages for typical textbooks currently used in college courses are 0 and 8 years. Use the range rule of thumb to estimate the standard deviation.
Standard deviation = I have gotten max - min / 4
= 8 - 0 / 4 = 2Find the size of the sample required to estimage the mean age of textbooks currently used in college courses. Assume that you want 98% confidence that the sample mean is within 0.4 year of the population mean.
Required sample size =
I have no clue how to get the required sample size
What are the correct answers?
1 Answer
$\begingroup$OK, now can apply Central Limit theorem if n is large enough. The thumb rule is $n>30$. We will see if it is the case. The width of the confidence interval is
$$\overline X+ z_{1-\frac{\alpha}{2}}\cdot \frac{s}{\sqrt n}-\left(\overline X- z_{1-\frac{\alpha}{2}}\cdot \frac{s}{\sqrt n}\right)=2\cdot z_{1-\frac{\alpha}{2}}\cdot \frac{s}{\sqrt n}$$
$\alpha$ is the significance level. Here it is $1-0.98=0.02$
$2\cdot z_{0.99}\cdot \frac{s}{\sqrt n}=0.4$
$2\cdot 2.33\cdot \frac{2}{\sqrt n}=0.4$
$\sqrt n=2\cdot 2.33\cdot \frac{2}{0.4}$
$\endgroup$ 9
