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ScotlandStatistics

Hypothesis Testing

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you test whether categorical data fit a model or whether two categorical variables are associated?

Carry out the chi-squared goodness-of-fit test and the chi-squared test for association in a contingency table, computing expected frequencies, the chi-squared statistic and degrees of freedom, and interpreting the result against the assumptions.
A focused answer to the SQA Advanced Higher Statistics chi-squared content: the goodness-of-fit test and the test for association in a contingency table, computing expected frequencies, the chi-squared statistic and degrees of freedom, the minimum expected frequency rule, and interpreting the outcome.
13 min answer →

How do you set up a hypothesis test and decide whether to reject the null hypothesis?

Set up null and alternative hypotheses, choose a significance level, compute and use a test statistic and p-value, decide between one- and two-tailed tests, identify the critical region, and distinguish Type I and Type II errors.
A focused answer to the SQA Advanced Higher Statistics hypothesis testing framework: forming null and alternative hypotheses, the significance level, the test statistic, the p-value and critical region, one- and two-tailed tests, and Type I and Type II errors.
12 min answer →

How do you test for a difference when the data are not normal or are ranks?

Carry out the main non-parametric tests, including the Mann-Whitney U test for two independent samples and the Wilcoxon signed-rank test for paired or single samples, explaining when a non-parametric test is preferred over a t-test.
A focused answer to the SQA Advanced Higher Statistics non-parametric test content: the Mann-Whitney U test for two independent samples and the Wilcoxon signed-rank test for paired data, how each ranks the data, the assumptions they relax, and when to prefer them over a t-test.
13 min answer →

How do you test a claim about a population proportion, or compare two proportions?

Carry out hypothesis tests for a single population proportion and for the difference between two proportions, using the normal approximation, stating the hypotheses, computing the test statistic and interpreting the result.
A focused answer to the SQA Advanced Higher Statistics proportion test content: testing a single population proportion and the difference between two proportions using the normal approximation, with the test statistics, the pooled estimate for two samples, and how to interpret the outcome.
12 min answer →

How do you test claims about one or two population means when the standard deviation is unknown?

Carry out the one-sample, two-sample (independent) and paired t-tests for population means, stating the hypotheses, computing the test statistic, using degrees of freedom, and interpreting the result, while checking the normality assumption.
A focused answer to the SQA Advanced Higher Statistics t-test content: the one-sample t-test, the two-sample (independent) t-test and the paired t-test, with the test statistics, the degrees of freedom, the normality assumption and how to interpret the outcome.
13 min answer →