Question

Professor Pierson wants to see if recording Zoom videos of practice problem solutions has any affect on quiz grades. Twenty students are given a quiz before the video is posted and a similar quiz a few days after. The mean difference in scores is 6.13 points with an estimate of the standard error of the mean difference of 1.91 points. Assume you are working at the 0.05 level of significance. What is the critical value for this test? O A. t = 1.96 OB. t = 2.093 OC. t = 3.209 O D. t = 2.086 Reset Selection

Answer 1

Here we have 20 students.

So n = 20

We want to test whether zoom videos of practice problems has any effect or not

So

$H_0: \mu_d = 0$

vs

$H_1: \mu_d \neq 0$

degrees of freedom = n-1 = 20 -1 = 19

So for 19 degrees of freedom, at a 5% level of significance and for a two-tailed test

Critical value = t = 2.093

Answer (B)

Now here estimate of mean difference = 6.13

and standard error = 1.91

So calculated value of t

$\frac{6.13}{1.91}$

= 3.209

As the calculated value of t is greater than the Critical value

We reject H0 at 5% level of significance.

Type -1 Error is our level of significance.

So Answer (A)

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