1. MATH 2311-06 Section 7.4 Pt. 2

2. Recall:

3. Look at the following example: The effect of exercise on the amount of lactic acid in the blood was examined in an article for an exercise and sport magazine. Eight males were selected at random from those attending a week-long training camp. Blood lactate levels were measured before and after playing three games of racquetball, as shown in the accompanying table. Use this data to estimate the mean increase in blood lactate level using a 95% confidence interval.

4. Values to cut and paste: assign(“before”,c(13,20,17,13,13,16,15,16)) assign(“after”,c(18,37,40,35,30,20,33,19))

5. t-score table:

6. Since n = 8, we are going to use the value for n – 1 = 7 degrees of freedom. Since we want a confidence level of 95%, we will use an “Upper Tail Probability” of (1 – 0.95)/2 = 0.025. This is to account for only using one tail end of our graph, rather than 2. Our t* value will be 2.3646.

7. Confidence Interval Calculation:

8. Interpretation of the Confidence Interval:

9. Example: A 95% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit. A preliminary sample standard deviation is 2.9. Find the he smallest sample size n that provides the desired accuracy.

10. Popper 23: A group of 10 students are comparing exam scores for a test they recently took. Based on these results, you want to find out, with 90% confidence, what range of grades you can expect to receive. Exam Scores:70, 75, 80, 87, 90, 90, 93, 94, 96, 100 1. What is the sample mean? a. 90b. 87.5c. 80d. 91.6 2. What is the sample standard deviation? a. 9.62b. 92.5c. 5.65d. 13.83 3. What is the t* value that can be used here? a. 1.3722b. 1.3968c. 1.8331d. 1.6449 4. What is the margin of error? a. 5.58b. 5.00c. 4.03d. 6.12 5. What is the confidence interval? a. [70,100]b. [87.5, 100]c. [85.67, 89.33]d. [81.65, 93.35]