- When you construct a 95% confidence interval, what are you 95% confident about?
- All other things remaining the same, is a 90% confidence interval narrower or wider than a 95% confidence interval? Briefly and clearly explain your answer.
**HINT:**Think of the corresponding margins of error (or error bounds). - All other things remaining the same, what is the impact of an increase in sample size on the width of the confidence interval? Explain your answer briefly and clearly.
- Briefly,

- compare the Z-distribution with Student’s t-distribution (t-distribution), focusing on the four attributes of probability distributions (random variable name, behavior [curve], mean, and standard deviation).
- compare the format of the Z-table with that of the t-table, focusing on the fundamental differences in format and the information involved.

- Briefly answer the following questions:

- When should we use the t-table, instead of the Z-table, while constructing confidence intervals or conducting tests of hypotheses.
- When must the requirement of the normality (or approximate normality) of the population distribution be met when we use Z or t?
- What would be the impact on the confidence interval, if a mistake is made and Z table is used instead of the t-table? Support your answer with a brief description and/or computation.
**HINT:**Examine the superimposed graphs of Z-distribution and t-distribution given in Lane, and focus on the relative magnitudes of Z_{a}_{/2 }and t_{a}_{/2}, each being a factor in the margin of error (error bound).

- (Show your work.) In a recent Zogby International Poll, nine of 48 respondents rated the likelihood of a terrorist attack in their community as “likely” or “very likely.”

- Use the “plus four” method, as explained by Illowsky, to create a 97% confidence interval for the proportion of American adults who believe that a terrorist attack in their community is likely or very likely.
- Explain what this confidence interval means in the context of the problem.