Estimation and Tests of Hypotheses for One Population

4-1 Mean and Standard Deviation of the Sampling Distribution of the Sample Mean, p. 275
- define, and use in context, the following key terms: population distribution; sampling distribution; sampling error and non-sampling error; mean and standard deviation of sampling distributions of the sample mean
  - Sampling distribution, sampling error, and nonsampling error
    - population probability distribution
    - sampling distribution
    - sampling and nonsampling errors
- find the mean and standard deviation of the sampling distribution of the sample mean, given the mean and standard deviation of the population distribution, and given the sample size.
  - Mean and Standard deviation of $\bar{x}$ .
4-2 Shape of the Sampling Distribution of the Sample Mean, p. 283
- state the Central Limit theorem and apply it to problems involving sample means.
  - Central limit theorem
  - Applications of the sampling distribution of $\bar{x}$
    - z value for a value of $\bar{x}$
- determine the shape of the sampling distribution of the sample mean, given information about the population distribution, the sample size, or both.
  - Shape of the sampling distribution of $\bar{x}$
- find the probability that the value of the sample mean will fall within a specified interval, given the population mean, the population standard deviation and the sample size.
  - Sampling from a normally distributed population
  - Sampling from a population that is not normally distributed
4-3 Mean, Standard Deviation, and Shape of the Sampling Distribution of the Sample Proportion, p. 293
- define, and use in context, the following key terms: population proportion and sample proportion; sampling distribution of the sample proportion; mean and standard deviation of the sampling distribution of the sample proportion; Central Limit theorem for sample proportions
  - Population and sample proportions;
  - Sampling distribution of $\hat{p}$
  - Mean and standard deviation of $\hat{p}$
- determine the mean, standard deviation and shape of the sampling distribution of the sample proportion, given the population proportion and the sample size.
  - Shape of the sampling distribution of $\bar{p}$ ?
    - $\hat{p}$
- find the probability that the value of the sample proportion will fall within a specified interval, given the population proportion and the sample size.
- Applications of the sampling distribution of $\hat{p}$
4-4 Estimation of a Population Mean: Population Standard Deviation Is Known, p. 311
- define, and use in context, the following key terms: point estimates and interval estimates; significance level; confidence level and confidence interval; margin of error
  - Estimation
  - Point and interval estimates
- use the z distribution to construct a confidence interval for the population mean when the population standard deviation is known, the population distribution is normal and the sample size is small (<30).
  - Estimation of a population mean: standard deviation known
    - $σ$
- use the z distribution to construct a confidence interval for the population mean when the population standard deviation is known and the sample size is large (≥30).
- compute the sample size that will be required to estimate the mean, given the confidence level, the population standard deviation and a specified margin of error.
4-5 Estimation of a Population Mean: Population Standard Deviation Is Unknown, p. 323
- define, and use in context, the following key terms: t distribution; sample standard deviation
  - The t distribution
- use the t distribution to construct a confidence interval for the population mean when the population standard deviation is unknown, the population distribution is normal and the sample size is small (<30).
  - Confidence interval for mu using the t distribution
    - $μ$
- use the t distribution to construct a confidence interval for the population mean when the population standard deviation is unknown and the sample size is large (≥30).
4-6 Estimation of a Population Proportion: Large Samples, p. 330
- define and apply the "estimator of the standard deviation of the sampling distribution of the sample proportion."
- use the z distribution to construct a confidence interval for the population proportion, given sample data.
- compute the sample size that will be required to estimate the proportion, given the level of confidence and a specified margin of error.
  - Determining the sample size for the estimation of proportion
4-7 Hypothesis Tests about a Single Population Mean: Population Standard Deviation Is Known, p. 346
- define, and use in context, the following key terms: null hypothesis; alternative hypothesis; critical value; Type I error; level of significance; Type II error; two-tailed test; right-tailed test; test statistic or observed value; statistically significantly different and statistically not significantly different; p-value
  - 2 Hypotheses
  - Rejection and nonrejection regions
  - 2 Types of errors
- use the critical value approach to perform a hypothesis test about the population mean, given the population standard deviation and sample data.
- use the p-value approach to perform a hypothesis test about the population mean, given the population standard deviation and sample data.
  - Tails of a test
    - The p-value approach
    - The critical-value approach
- Added: The p-Value Approach, The Critical-Value Approach, The p-Value and Critical Value Approaches
  - Study Guide
4-8 Hypothesis Tests about a Single Population Mean: Population Standard Deviation Is Unknown, p. 367
- use the critical value approach to perform a hypothesis test about the population mean, given sample data, when the population standard deviation is unknown.
  - The critical-value approach
- The p-value approach
- Added: Estimating the p-Value for the t Distribution of Two-Tailed Tests; Estimating the p-Value for the t Distribution of One-Tailed Tests.
  - Study Guide
4-9 Hypothesis Tests about a Single Population Proportion: Large Samples, p. 375
- Use the critical value approach and the p-value approach to perform a hypothesis test about the population proportion, given data from a large sample.
  - The critical-value approach
  - The p-value approach