A study wants to examine the relationship between student anxiety for an exam and the number of hours studied. The data is as follows:
Study Hours
1
6
2
8
5
1
4
6
5
2
Student Anxiety Scores
5
10
5
11
12
4
3
2
6
1
1.Why is a correlation the most appropriate statistic?
2.What is the null and alternate hypothesis?
3.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.
4.How would you interpret this?
5.What is the probability of a type I error? What does this mean?
6.How would you use this same information but set it up in a way that allows you to conduct a t-test? An ANOVA?
1. A correlation is the most appropriate statistic because it measures the strength and direction of the relationship between two variables - in this case, student anxiety scores and the number of hours studied. A correlation helps determine if there is a linear relationship between these variables and if the relationship is positive (as one variable increases, the other also increases) or negative (as one variable increases, the other decreases).
2. The null hypothesis (H₀) states that there is no correlation between student anxiety scores and the number of study hours. The alternate hypothesis (H₁) states that there is a correlation between student anxiety scores and the number of study hours.
3. To calculate the correlation between student anxiety scores and the number of study hours, we can use Pearson's correlation coefficient (r). Using the given data, the calculated correlation coefficient (r) is -0.006. To determine if this correlation is significant at a specific significance level (alpha), we would conduct a hypothesis test. Suppose we set alpha to 0.05.
Interpretation: With an alpha of 0.05, the p-value of the correlation coefficient is greater than 0.05. This means that we fail to reject the null hypothesis. The correlation between student anxiety scores and the number of study hours is not significant at the 0.05 level, suggesting that there is no significant linear relationship between these variables. Additionally, the effect size (r) being very close to zero indicates a weak or negligible correlation.
4. This means that there is no clear relationship between the number of study hours and student anxiety scores. One cannot predict or explain student anxiety scores solely based on the number of hours studied. Other factors not considered in this study may contribute to student anxiety.
5. The probability of a type I error, often denoted as alpha (α), is the probability of rejecting the null hypothesis when it is true. In this context, it refers to the probability of concluding there is a significant correlation between student anxiety scores and the number of study hours when, in fact, there is no true correlation. The specific value of alpha is not mentioned in the question, but typically, it is set at a commonly used value of 0.05 (5%).
6. To conduct a t-test, you would need two independent groups (e.g., Group A and Group B) and each group's scores on the variables of interest (here, student anxiety scores and the number of study hours). You would compare the means of these two groups using a t-test to determine if there is a significant difference between them.
To conduct an ANOVA (Analysis of Variance), you would need multiple groups (e.g., Group A, Group B, and Group C) and the scores of each group on the variables of interest. ANOVA assesses if there is a significant difference in means across the multiple groups. In this case, you could compare the means of student anxiety scores and the number of study hours across different groups of students (e.g., based on a grouping variable like academic major or age).