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.