What potential problems should you look for in the univariate distributions of categorical and quantitative scores?

Studies show that the level of anxiety has changed since the pandemic. The average score before the pandemic was mu equal to 36. A sample of 20 individuals surveyed in the past two weeks produced M=37.6 and s=9.8. Based on the sample, was there a significant difference in the average anxiety level since the pandemic started at the 5% significance level? What is the positive critical value?   (a)2.093 (b)2.086   (c)1.729   (d)1.725

In a simple linear regression, given that the sample variances of x and y Sx^2=510, Sy^2=750 respectively, cov(x, y)=100 and n = 10. What is the standard error of estimate? Round your answer to the nearest third decimal.

At the Thanksgiving break, I measured the correlation between the pre-class quiz grade and the average grade in the class for all 33 students in my stats classes. Below is the output from those results.  Correlation  Pearson correlation of PreClass and Grade = 0.705630  P-Value = < 0.0001  Regression Equation  Grade = 0.24333 + 0.006369 PreClass    (a) Determine the critical value in the table and explain how you know these two variables would be considered correlated.    (b) Knowing that there is correlation, use this model to predict the average grade of a student in this class who did not complete any pre-class quizzes.    (c) Assuming everyone in this class completed at least one quiz, would you describe the previous problem as interpolation or extrapolation?