MATH 215 Introduction to Statistics study guide

Organize, display, summarize, and interpret qualitative and quantitative data.

• 1.1 · Use basic statistical terms and notation (published written lesson)
• 1.2 · Classify variables and types of data (published written lesson)
• 1.3 · Distinguish populations, samples, experiments, and summation notation (published written lesson)
• 1.4 · Organize and graph qualitative data (published written lesson)
• 1.5 · Organize and graph quantitative data (published written lesson)
• 1.6 · Calculate and interpret measures of centre for ungrouped data (published written lesson)
• 1.7 · Calculate and interpret dispersion for ungrouped data (published written lesson)
• 1.8 · Estimate the mean, variance, and standard deviation for grouped data (published written lesson)
• 1.9 · Use standard deviation to describe and compare data (published written lesson)
• 1.10 · Use measures of position and box plots (published written lesson)

Model chance processes with sample spaces, probability rules, and counting methods.

• 2.1 · Describe experiments, outcomes, events, and sample spaces (written lesson not published)
• 2.2 · Compare classical, empirical, and subjective probability (written lesson not published)
• 2.3 · Calculate marginal and conditional probabilities (written lesson not published)
• 2.4 · Find intersections using the multiplication rule (written lesson not published)
• 2.5 · Find unions using the addition rule (written lesson not published)
• 2.6 · Use counting rules, factorials, and combinations (written lesson not published)

Work with discrete random variables, binomial models, and normal distributions.

• 3.1 · Build probability distributions for discrete random variables (written lesson not published)
• 3.2 · Find the mean and standard deviation of a discrete random variable (written lesson not published)
• 3.3 · Recognize and solve binomial probability problems (written lesson not published)
• 3.4 · Use the standard normal distribution and z-scores (written lesson not published)
• 3.5 · Solve probability problems with normal distributions (written lesson not published)
• 3.6 · Approximate binomial probabilities with a normal distribution (written lesson not published)

Use sampling distributions, confidence intervals, and hypothesis tests for one population.

• 4.1 · Find the mean and standard deviation of the sample-mean distribution (written lesson not published)
• 4.2 · Determine the shape of the sample-mean distribution (written lesson not published)
• 4.3 · Use the sampling distribution of a sample proportion (written lesson not published)
• 4.4 · Construct a confidence interval for a mean when population standard deviation is known (written lesson not published)
• 4.5 · Construct a confidence interval for a mean when population standard deviation is unknown (written lesson not published)
• 4.6 · Construct a large-sample confidence interval for a population proportion (written lesson not published)
• 4.7 · Test a population mean when population standard deviation is known (written lesson not published)
• 4.8 · Test a population mean when population standard deviation is unknown (written lesson not published)
• 4.9 · Test a population proportion with a large sample (written lesson not published)

Compare means, proportions, variances, distributions, and several group means.

• 5.1 · Compare two independent means when population standard deviations are known (written lesson not published)
• 5.2 · Compare two independent means when population standard deviations are unknown but equal (written lesson not published)
• 5.3 · Compare two means using paired data (written lesson not published)
• 5.4 · Compare two population proportions (written lesson not published)
• 5.5 · Perform a chi-square goodness-of-fit test (written lesson not published)
• 5.6 · Test independence or homogeneity with a contingency table (written lesson not published)
• 5.7 · Make inferences about a population variance (written lesson not published)
• 5.8 · Compare several population means using one-way analysis of variance (written lesson not published)

Describe and assess linear relationships using regression and correlation.

• 6.1 · Fit and interpret a simple linear regression model (written lesson not published)
• 6.2 · Interpret residual standard deviation and the coefficient of determination (written lesson not published)
• 6.3 · Make inferences about the simple linear regression slope (written lesson not published)
• 6.4 · Calculate and interpret linear correlation (written lesson not published)
• 6.5 · Apply correlation and regression while recognizing their limitations (written lesson not published)

Find the sample mean of 4, 7, 7, 10, and 12.

Worked method: The sum is 40 and n = 5, so x̄ = 40/5 = 8. In context, the sample average is 8 units.

Of 80 students, 32 study online; 20 of those online students work full time. Find P(full time | online).

Worked method: Restrict the denominator to online students: 20/32 = 0.625. Thus 62.5% of the online students in this sample work full time.

A 95% confidence interval for a population mean is (18.2, 21.6). Interpret it.

Worked method: Using this method, we are 95% confident that the population mean lies between 18.2 and 21.6. The statement concerns the unknown population mean, not 95% of individual observations.

A fair die is rolled once. Find the probability of an even result.

A z-score is 1.25. Is the observation above or below the mean, and by how many standard deviations?