Q 8.79 - Elementary Statistics

Question

Medical Marijuana. Refer to Exercise 8.77.

a. Determine the margin of error for the $95\%$ confidence interval.

b. Determine the margin of error for the $90\%$ confidence interval.

c. Compare the margins of error found in parts (a) and (b).

d. What principle is being illustrated?

Step-by-Step Solution

Answer

a. The margin of error is $5.726$.

b. The margin of error is $4.805$.

c. The margin of error of $90\%$ confidence interval is greater than $95\%$ confidence interval.

d. The principle of same sample size and decrease in confidence level is illustrated.

Step 1: Given Information

Confidence level of $90\%$ and $95\%$ are given.

Step 2: Margin of Error for 95 % confidence interval

From exercise 8.77, it can be observed that $95\%$ confidence interval for $\mu$ is $\left(96.994, 108.446\right)$

Margin of error is calculated as:

$E=\frac{108.416-96.994}{2}$

$=\frac{11.452}{2}$

$E=5.726$

Step 3: Margin of Error for 90 % Confidence Interval

From 8.77, $90\%$ confidence interval for $\mu$ is $(97.915 .107 .525)$

Margin of Error is calculated as

$E=\frac{107.525-97.915}{2}$

$E=\frac{9.61}{2}$

$E=4.805$

Step 4: Which Margin of Error is Less

From above calculations, it is clear that margin of error for $90\%$ confidence interval is smaller as compared to $95\%$ confidence interval.

Step 5: The Principle illustrated

The principle illustrated is:

"Same Sample Size and Decrease in Confidence Level, hence Decreasing Margin of Error".