Question

After deciding on a $95\%$ confidence level, the researcher is deciding between a sample of size $n=500$ and a sample of size $n=1000$. Compared with using a sample size of $n=500$, a confidence interval based on a sample size of $n=1000$ will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. narrower and would have the same risk of being incorrect.

Short answer

Option (e) is correct.

Step-by-step solution

Given Information

Two sample sizes are given$n=500,n=1000$

Explanation

The confidence interval is related to sample size negatively. If sample size increases, precision of confidence interval lowers risk of being correct.

If sample size $1000$is used at same $95\%$confidence interval, confidence interval is less and there is same risk for being incorrect.