Stats for Beginners

Enter and organize a small dataset in Excel using labels, values, cell references, and basic formulas.

Create a frequency table and histogram from raw data in Excel.

Calculate and interpret the mean, median, and mode of a dataset.

Calculate and interpret the range, variance, and standard deviation of a dataset.

Use Excel functions to calculate measures of center and variation.

Calculate a z-score and use it to compare relative positions in different datasets.

Calculate quartiles and the interquartile range, apply the 1.5 × IQR rule, and display the results in a boxplot.

Choose and justify numerical and graphical summaries based on variable type, distribution shape, and outliers.

Represent the possible outcomes of a chance process with a sample space and events.

Calculate the probability of an event's complement.

Apply the general addition rule and recognize when two events are mutually exclusive.

Calculate conditional probabilities from counts or a two-way table.

Apply the multiplication rule to calculate the probability of a sequence of events.

Determine whether two events are independent using probabilities or a two-way table.

Organize multistage probabilities with a tree diagram or table.

Calculate the number of possible outcomes using the fundamental counting rule and factorials.

Calculate permutations and combinations for ordered and unordered selections.

Determine whether to use the fundamental counting rule, permutations, or combinations in a counting problem.

Verify that a table defines a valid discrete probability distribution.

Calculate the mean, variance, and standard deviation of a discrete random variable.

Determine whether a scenario satisfies the requirements of a binomial experiment.

Calculate an exact binomial probability using the binomial formula and a basic calculator.

Calculate exact and cumulative binomial probabilities with Excel and the complement rule.

Use a binomial distribution's mean and standard deviation to identify unusual results.

Determine whether a count scenario can be modeled with a Poisson distribution and identify its rate parameter.

Calculate and interpret a Poisson probability using a basic calculator or Excel.

Identify the center, spread, and symmetry of a normal distribution from its parameters and graph.

Translate a verbal normal-probability question into a labeled sketch with the correct region shaded.

Use a standard normal table to find an area or probability from a z-score.

Find a z-score corresponding to a given cumulative area or percentile.

Calculate probabilities for a nonstandard normal variable.

Find a cutoff value or percentile in a nonstandard normal distribution.

Assess approximate normality using a histogram and a normal quantile plot.

Distinguish a population distribution, a sample distribution, and a sampling distribution.

Calculate the mean and standard error of a sample-mean distribution.

Use the Central Limit Theorem and relevant conditions to determine when a sample-mean distribution is approximately normal.

Calculate a probability involving a sample mean.

Check independence and large-count conditions and calculate the mean and standard error of a sample-proportion distribution.

Calculate a probability involving a sample proportion.

Predict how increasing sample size changes sampling variability.

Interpret a confidence level and confidence interval in the context of repeated sampling.

Find standard normal and Student t critical values, including the appropriate degrees of freedom, for a specified confidence level.

Check the conditions required for a one-sample confidence interval for a population mean.

Construct and interpret a one-sample confidence interval for a population mean using the t distribution.

Check the conditions required for a one-sample confidence interval for a population proportion.

Construct and interpret a one-sample confidence interval for a population proportion.

Determine a sample size needed to estimate a mean or proportion with a specified margin of error.

Use Excel confidence-interval output to report an estimate in context.

Translate a verbal claim into null and alternative hypotheses and identify the test direction.

Distinguish Type I and Type II errors in the context of a decision.

Relate a significance level, test statistic, reference distribution, and p-value.

Use a p-value to make a significance decision and state the conclusion in the language of the original claim.

Check conditions and conduct a one-sample t test for a population mean using a permitted basic calculator.

Check conditions and conduct a one-sample z test for a population proportion using a permitted basic calculator.

Use Excel formulas or provided Excel output to conduct and document a one-sample hypothesis test.

Distinguish statistical significance from practical significance.

Distinguish independent samples from paired data in a study description.

Check conditions and construct a confidence interval for the difference between two population proportions.

Conduct and interpret a hypothesis test comparing two population proportions.

Check conditions and construct a confidence interval for the difference between two independent population means.

Conduct and interpret a hypothesis test comparing two independent population means.

Convert paired observations into a single sample of differences and check its conditions.

Carry out the requested paired t confidence interval or hypothesis test and interpret the result in context.

Select the appropriate two-sample procedure for a given study design and variable type.

Create and interpret a scatterplot for two quantitative variables.

Calculate and interpret the direction and strength of a linear correlation coefficient.

Explain why correlation does not by itself establish causation.

Conduct and interpret a hypothesis test for linear correlation.

Fit a least-squares regression line using Excel.

Interpret the slope and intercept of a regression line in context.

Use a regression equation for prediction while recognizing extrapolation.

Assess a regression model using residuals, influential outliers, and the coefficient of determination.

Distinguish a chi-square goodness-of-fit question from a chi-square test-of-independence question.

Calculate expected counts and check the conditions for a chi-square goodness-of-fit test.

Conduct and interpret a chi-square goodness-of-fit test.

Calculate expected counts in a contingency table and check the conditions for a chi-square test of independence.

Conduct and interpret a chi-square test of independence.

State the hypotheses of a one-way analysis of variance in context.

Check the independence, approximate normality, and equal-variation conditions for one-way ANOVA.

Conduct a one-way ANOVA in Excel and use its F statistic and p-value to conclude whether there is evidence that at least one population mean differs.

Translate a statistical word problem into known quantities, an unknown target, and relevant variables.

Select an appropriate descriptive or inferential method from the full STAT 1P98 toolkit.

Verify the assumptions and conditions for a selected statistical procedure using a checklist.

Carry out a probability or inference calculation with a permitted basic calculator while showing all required steps.

Check whether a statistical calculation is plausible using estimation, units, and probability bounds.

Use Excel to generate and clearly label the output required for a structured statistical analysis.

Write a concise, plain-language interpretation of statistical output without overstating the evidence.

Complete a short timed set of mixed STAT 1P98 problems, then diagnose and correct conceptual or computational errors.