Question 8 of 10 , Step 3 of 4 A certain test preparation course is designed to help students improve their scores on the GRE exam. 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 students' scores on the exam after completing the course: 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. 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, we need to determine the z-score or t-score corresponding to the significance level of 0.20 (since 1 - 0.80 = 0.20). For a two-tailed test, we divide the significance level by 2, which gives us 0.10. Looking up the z-value for 0.10 in the standard normal distribution table, we find that the critical value is approximately \( z = 1.282 \). Since you have 7 students, using the t-distribution is more appropriate. With 6 degrees of freedom (n-1 = 7-1), the t-score corresponding to an 80% confidence level is about \( t = 1.440 \). Therefore, the critical value to use in constructing the confidence interval is approximately \( t = 1.440\) when rounded to three decimal places. This gives you the critical value necessary for calculating the confidence interval around the mean net change in scores! Just remember that using the t-table means you've got to think about sample size and degrees of freedom so the results really reflect your sample.