smo \& brt Corily Question 8 of 10,5 tep 3 of 4 14/19 Correct A certain test preparation course is designed to help students improve their scores on the GRE sxam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 7 student's scores on the exam after completing the course: \[ 24,6,21,8,16,10,18 \] Using these data, construct a \( 80 \% \) confidence interval for the average net change in a student's score' after completing the course. Assume the population is approximately normal. Copy Data Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval, Round your answer to three decimal places.

To find the critical value for an 80% confidence interval, you first need to determine the significance level (α), which is 1 - 0.80 = 0.20. Since this is a two-tailed test, you'll divide the significance level by 2, resulting in α/2 = 0.10. Using a t-distribution table and the sample size (n = 7), you'll have degrees of freedom (df) at n - 1 = 6. The critical value corresponding to df = 6 and α/2 = 0.10 is approximately 1.943. Be sure to round it to three decimal places, giving you a final critical value of 1.943. Now that you have the critical value, plug it into your confidence interval formula! This value will help you determine the margin of error for your average net change in GRE scores, giving you a sense of confidence in your results. Keep in mind that the smaller the confidence level, the larger the critical value you may need to compensate for reduced uncertainty in your estimates. Happy calculating!