Section 6.2: Estimating a Population Proportion

1. State the large-sample margin of error for the sample proportion $\widehat{p}$ in terms of the population proportion $p$.
2. State the large-sample confidence interval for the population proportion $p$
3. Determine the large-sample confidence interval to use depending on when a pilot estimate of $p$ is known or unknown.
4. Given a sample size $n$, sample proportion $\widehat{p}$, and confidence level $c$, construct a $100c\%$ confidence interval for the population proportion $p$.
5. Given a confidence level $c$ and a desired precision $E$, determine the sample size necessary to attain that level of precision at that confidence level.
6. Explain, qualitatively, how the precision of the sample proportion varies with the confidence level $c$, sample size $n$, and population proportion $p$.

Section 10.2: Multinomial Experiments: Goodness-of-Fit

1. Relate a multinomial procedure to a binomial procedure.
2. State the requirements necessary for the outcome of an procedure to follow a multinomial distribution.
3. State examples from everyday life that follow a multinomial distribution.
4. State the definition of a goodness-of-fit test.
5. Explain, qualitatively, how the $\chi^{2}$ statistic compares the observed outcomes to the expected outcomes in a multinomial procedure.
6. State the large-sample sampling distribution of the $\chi^{2}$ statistic under the null hypothesis for a multinomial procedure with $k$ categories for the outcomes.
7. State conditions on the expected frequencies for when the $\chi^{2}$ statistic can be used.
8. Use Table A–4 to determine critical values for a one-sample $\chi^{2}$ test for goodness-of-fit at significance level $\alpha$.
9. Use Minitab to perform a one-sample $\chi^{2}$ test for goodness-of-fit.
10. Interpret the output of a one-sample $\chi^{2}$ test for goodness-of-fit in terms of a given null and alternative hypotheses.