Week 4 LEO Discussion Topic Exercise Confidence Interval (Test Scores) Group Learning Outcomes The group will calculate the 90% confidence interval for the mean test score on a recent inferential statistics test. The group will interpret confidence intervals. The group will determine the effects of changing conditions on the confidence interval. Review the Data The following table lists scores attained by 35 students taking a recent inferential statistics test: 73 68 79 90 74 66 91 85 71 66 81 80 92 75 69 82 95 80 83 77 77 72 76 72 73 69 74 59 78 70 75 70 99 88 91 Describe the Data 1. Compute the following: 2. a. x = b. s x = c. n= In words, define: X . a. the random variable b. the estimated distribution to use. Use both words and symbols. Find the Confidence Interval 3. Calculate the confidence interval and the error bound (EBM): 1 Week 4 LEO Discussion Topic Exercise a. Confidence Interval: _____ b. Error Bound (EBM): _____ 4. a. How much area is in both tails (combined)? b. How much area is in each tail? = /2= 5. Fill in the blanks on the graph with the area in each of the three sections (remember, the sum of the three areas = 1). Then, fill in the number line with the upper and lower limits of the confidence interval and the sample mean. Area 1 = ___________ Lower Limit = _____________ Area 2 = ____________ x = Area 3 = _____________ Upper Limit = ____________ 2 Week 4 LEO Discussion Topic Exercise 6. Some students think that a 90% confidence interval contains 90% of the data. Use the list of data on the first page and count how many of the data values lie within the confidence interval. What percent is this? Is this percent close to 90%? Explain why this percent should or should not be close to 90%. Describe the Confidence Interval 7. In two to three complete sentences, explain what a confidence interval means (in general), as if you were talking to someone who has not taken statistics. 8. In one to two complete sentences, explain what this confidence interval means for this particular study. Use the Data to Construct Confidence Intervals 9. Using the given information, construct a confidence interval for each confidence level given. Confidence Level 50% 80% 90% 95% Error Bound EBM Confidence Interval 10. What happens to the EBM as the confidence level increases? Does the width of the confidence interval increase or decrease? Explain why this happens. 3