Q.1.3 - The Practice of Statistics for AP

Question

True or false: The interval from $2.84$ to $7.55$ has a $95\%$ chance of containing the actual population standard deviation $S$. Justify your answer. 

Step-by-Step Solution

Answer

The provided statement is false.

Step 1: Given Information

Confidence interval $=(2.84,7.55)$,

Number of dogs $\left(n\right)=10$,

Confidence level $=95\%$.

Step 2: Explanation

The provided statement is, "The confidence interval from $2.84$ to $7.55$ has $95\%$ probability of capturing the true value of population standard deviation"

If the sampling procedure is repeated n number of times than $95\%$ of the computed confidence interval are expected to contain the standard deviation of population.

Thus, the provided statement is False.