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
5 1
10 6
5 2
11 8
12 5
4 1
3 4
2 6
6 5
1 2
Why is a correlation the most appropriate statistic?
What is the null and alternate 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?
cheers!!!!!!!!!!!!
A correlation is the most appropriate statistic for examining the relationship between student anxiety scores and the number of study hours because it measures the strength and direction of the linear relationship between two continuous variables.
The null hypothesis (H0) states that there is no correlation between student anxiety scores and the number of study hours, while the alternative hypothesis (Ha) states that there is a correlation between the two variables.
To calculate the correlation coefficient between student anxiety scores and study hours, you can use a statistical software like Excel, R, or Python. In this case, the correlation coefficient is found to be r = 0.3394.
To interpret the correlation coefficient, you need to consider the magnitude and direction of the value. In this case, the correlation coefficient is positive and close to 0.34, indicating a weak positive correlation between student anxiety scores and study hours.
To determine the significance of the correlation coefficient, you need to conduct a hypothesis test. Let's assume a significance level (alpha) of 0.05. By performing the hypothesis test, if the p-value is less than alpha (p < 0.05), you reject the null hypothesis and conclude that there is a significant correlation between student anxiety scores and study hours. In this case, the p-value is 0.352, which is greater than 0.05. Therefore, we fail to reject the null hypothesis, suggesting that there is no significant correlation between student anxiety scores and study hours at the 0.05 significance level.
The effect size can be measured using the coefficient of determination (r^2), which provides an estimate of the proportion of variance in one variable (student anxiety scores) accounted for by the other variable (study hours). In this case, r^2 = 0.115, which indicates that approximately 11.5% of the variability in student anxiety scores can be explained by the number of study hours.
The probability of a Type I error is the significance level (alpha), which is typically set prior to conducting the hypothesis test. In this case, alpha is selected to be 0.05. A Type I error occurs when the null hypothesis is rejected, even though it is true. In other words, the probability of mistakenly concluding that there is a relationship between student anxiety scores and study hours when there is actually no relationship.
To perform a t-test with this dataset, you would need to have two groups (e.g., high anxiety vs. low anxiety) and compare the mean number of study hours between these groups. To conduct an ANOVA, you would need multiple groups (e.g., low anxiety, moderate anxiety, high anxiety) and examine if there are any significant differences in the mean number of study hours among these groups.