Determine the relationship between the level of confidence and the required sample size: People were polled on how many books they read the previous year. Initial survey results indicate that $s=19.6$ books. Complete parts (a) through (d) below. Click the icon to view a partial table of critical values. Compare this result to part (a). How does increasing the level of confidence in the estimate affect sample size? Why is this reasonable? A. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a smaller sample size. B. Increasing the level of confidence decreases the sample size required. For a fixed margin of error, greater confidence can be achieved with a smaller sample size. C. Increasing the level of confidencefincreases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size. D. Increasing the level of confidence decreases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.
Solution
Step 1 ：The question is asking about the relationship between the level of confidence and the required sample size in a statistical study. It's a theoretical question and doesn't require any calculations.
Step 2 ：In statistics, the level of confidence refers to the probability that the confidence interval contains the true population parameter. The higher the level of confidence, the wider the confidence interval.
Step 3 ：The sample size is the number of observations in a sample. The larger the sample size, the more accurately it represents the population, and the narrower the confidence interval.
Step 4 ：Therefore, to maintain the same level of confidence, if we want to narrow the confidence interval (reduce the margin of error), we need to increase the sample size. Conversely, if we want to increase the level of confidence while keeping the same margin of error, we also need to increase the sample size.
Step 5 ：So, the correct answer should be that increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.
Step 6 ：Final Answer: \(\boxed{\text{C. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.}}\)
