PYC3704 Assignments Questions & Answers 2026/2027 | 40+ Questions | Research Methods, Probability, Z-Scores, Hypothesis Testing, T-Tests & Correlation

This PYC3704 Assignments 2026/2027 study resource contains 40+ questions with answers across 13 pages, providing focused revision of quantitative research and statistical analysis. The document covers measurement, variables, constructs, hypotheses, populations and samples, frequency distributions, probability, the law of large numbers, normal distributions, z-scores, standard error, statistical significance, null and alternative hypotheses, Type I and Type II errors, p-values, effect sizes, z-tests, t-tests, Pearson correlation, chi-square tests, and interpretation of scatterplots. It combines conceptual definitions with numerical and research-scenario questions, making it useful for assignment preparation, statistics revision, and exam-focused practice. The opening section concentrates on research methodology, measurement, and foundational statistical terminology. Students review inference as generalizing from a specific situation to a broader phenomenon, measurement as allocating numbers to observations according to a rule and operationalizing abstract constructs, and the distinction between a variable and a specific value of that variable. The guide also differentiates a population parameter from a sample statistic, defines hypotheses in relation to constructs, and uses a creativity study involving fine-arts students to illustrate the difference between a population and a sample. A substantial portion addresses probability and probability distributions through practical calculations. Examples include conditional selection from a group of students, probabilities involving examination marks, rolling dice, selecting colored marbles, and identifying only children from a sample. The document also reviews the law of large numbers, explaining through a coin-flipping example that increasing the number of trials should produce outcomes that increasingly approximate expected probabilities. Frequency and probability distributions are also incorporated into this section. The guide provides important coverage of the standard normal distribution and z-scores. Students review the horizontal scale of the standard normal distribution in terms of standard deviations above and below the mean and learn that z-scores allow comparison of scores obtained on tests with different means and standard deviations. One worked scenario uses a sample mean of 20 and standard deviation of 8 to calculate a z-score of −0.75 for a score of 14, followed by a probability question for obtaining a score of 14 or below. The inferential statistics and hypothesis-testing section is particularly detailed. The document explains the null hypothesis as assuming no relationship or difference between the parameters being tested and reviews comparison of a p-value with the selected significance level when making statistical decisions. Students examine α, statistical significance, Type I and Type II errors, and the consequences of selecting a stricter significance level such as α = 0.001 rather than α = 0.05. The source notes that this stricter threshold results in fewer rejections of the null hypothesis while increasing the likelihood of a Type II error. The material further explores p-values, statistical significance, and effect size. It presents p .05 in terms of the probability of obtaining the observed data if the null hypothesis were true and identifies effect size as important for evaluating the relative or practical importance of a relationship independently of sample size. The document recommends reporting information such as sample size, the exact p-value, effect size, and calculated test statistic so readers can evaluate statistical results more meaningfully. Students also review the selection and interpretation of z-tests and t-tests. The document identifies the one-sample t-test as appropriate when comparing a sample mean with a specified population value when the population standard deviation σ is unknown. It discusses using t-tests to compare two group means or a group mean with a constant value, explains independent samples, distinguishes one-tailed from two-tailed hypotheses, and uses a worked example involving t = 1.72 and a two-tailed p-value of 0.056 to illustrate adjustment for a directional hypothesis. The final sections focus on correlation and chi-square analysis. Pearson's correlation coefficient r is presented as ranging from −1 to +1 and describing a linear relationship between variables. Negative correlation is illustrated through examples involving anxiety and memory performance and blood-alcohol concentration and balance. The anxiety example, accompanied by a scatterplot scenario in the document, is interpreted as showing that as anxiety increases, fewer items are remembered, corresponding to an expected r 0. The chi-square test is introduced as a method for comparing observed frequency data with the distribution expected if the null hypothesis is true. The resource also uses a study of drug treatment and mental alertness among hospitalized patients to illustrate a correlational null hypothesis expressed as H₀: ρ = 0. Together, these examples help students connect statistical notation with realistic psychological research designs and data-analysis decisions. Relevant students: This resource is particularly relevant for PYC3704 students, psychology students, UNISA students, undergraduate research-methods students, quantitative research students, behavioural science students, social science students, and learners studying introductory and intermediate statistics. It is especially useful for students preparing assignments or examinations involving probability calculations, hypothesis testing, p-values, statistical significance, t-tests, correlations, chi-square tests, and interpretation of quantitative psychological research. Referenced academic source: Gravetter, F. J., Wallnau, L. B., Forzano, L. A. B., & Witnauer, J. E. Essentials of Statistics for the Behavioral Sciences. Cengage. This statistics reference is relevant to the document's major areas, including probability, sampling distributions, z-scores, hypothesis testing, statistical significance, t-tests, effect size, correlation, and chi-square analysis. 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