Assignment 1 Lasa 2: Conducting And Analyzing Statist 904815

Assignment 1 Lasa 2 Conducting And Analyzing Statistical Testsyour W

Your written presentation to the following problem situation should be a formal academic presentation wherein APA guidelines apply. A study wants to examine the relationship between student anxiety for an exam and the number of hours studied. The data is as follows: Student Anxiety Scores, Study Hours. Why is a correlation the most appropriate statistic? What is the null and alternative hypothesis? What is the correlation between student anxiety scores and number of study hours? Select alpha and interpret your findings. Make sure to note whether it is significant or not and what the effect size is. How would you interpret this? What is the probability of a Type I error? What does this mean? How would you use this same information but set it up in a way that allows you to conduct a t-test? An ANOVA?

Paper For Above instruction

The investigation into the relationship between student anxiety scores and the number of hours studied necessitates a statistical approach that accurately captures the association between these two variables. A correlation coefficient, specifically Pearson’s r, is most appropriate in this context because it measures the strength and direction of a linear relationship between two continuous variables. Both anxiety scores and study hours are continuous variables, making correlation an ideal choice to assess whether increased study time correlates with decreased or increased anxiety levels among students.

The null hypothesis (H₀) asserts that there is no relationship between student anxiety scores and study hours, expressed mathematically as H₀: ρ = 0, where ρ denotes the population correlation coefficient. The alternative hypothesis (H₁) posits that a significant relationship exists, expressed as H₁: ρ ≠ 0. Depending on the direction of the observed relationship, one might specify a one-tailed test, but in most cases, a two-tailed test is appropriate to identify any correlation regardless of its direction.

If the data were available, the correlation coefficient could be computed, providing a value between -1 and 1. For instance, suppose the analysis yields a correlation of r = -0.45. This indicates a moderate negative relationship; as study hours increase, student anxiety tends to decrease. To interpret the significance of this correlation, an alpha level (α) must be chosen—commonly 0.05. If the p-value associated with the correlation is less than α, the correlation is statistically significant, suggesting a real association in the population.

Effect size, measured by the magnitude of r, informs us about the strength of this association. An r of -0.45 suggests a moderate effect size, as per Cohen’s guidelines. This indicates that about 20% of the variability in student anxiety scores can be explained by the number of hours studied, since r² = 0.20. Such an effect has practical implications, implying that increasing study hours might help reduce anxiety among students.

The probability of committing a Type I error—that is, rejecting the null hypothesis when it is actually true—is equal to the alpha level, set at 0.05. This indicates a 5% risk of a false positive, where the analysis suggests a relationship exists when it does not in reality. Understanding this probability helps researchers balance the risks of false positives with the need to detect genuine effects.

Alternatively, if the goal was to compare mean anxiety scores between two groups, such as students who studied a high number of hours versus those who studied fewer hours, a t-test would be appropriate. To set this up, the data should be categorized into two independent groups based on study hours, and the mean anxiety scores of these groups would be compared using an independent samples t-test. This test evaluates whether the difference in mean anxiety scores between the two groups is statistically significant.

Similarly, if the research involved more than two groups—for example, students who studied for 0-2 hours, 3-5 hours, and more than 6 hours—an ANOVA (Analysis of Variance) could be employed. ANOVA examines whether there are statistically significant differences in mean anxiety scores across multiple groups. It is an extension of the t-test that handles more than two group comparisons simultaneously, controlling for type I error inflation.

References

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