Dr. Loizeaux

STAT 350 (Spring 2017) Homework 9 (20 points + 1 point BONUS) 1

Practice Problems: 10.1 (p. 471), 10.3 (p. 471), 10.5 (p. 471), 10.31 (p.485), 10.35 (p.485), 10.67 (p.497), 10.69 (p.497)

(10 pts. + 1 pt. BONUS) 1. In 1969, the height of Major League Baseball pitching mounds was

lowered from 15 to 10 inches. This decreased a pitcher’s leverage and presumably the speed of a typical fastball. Fifteen Major League pitchers were selected at random, and each threw fastballs from both a 15-inch mound and from a 10-inch mound. A coin was flipped to determine which mound height was used first. The speed of each pitch (in mph) was recorded and the average of ten pitches was taken and recorded. Note that this is not a blind test because the pitchers can tell the height of the mound before they pitch the ball. Please assume that the distribution is normal. The summary data are given in the following table.

Measure n x̄ s

Average Speeds recorded from 15-inch mounds 15 89.27 4.621

Average Speeds recorded from 10-inch mounds 15 86.47 2.588

Differences in speeds (speed on 15-inch – speed on 10-inch) 15 2.8 4.109

(1 pt.) a) Should this situation be analyzed via a 2-sample independent or paired method?

Please explain your answer. (6 pts.) b) Is there any evidence to suggest the true mean speed is larger for mounds that are

15 in high versus mounds that are 10 inches high? Use = 0.05. Remember to include the complete 4-step method in the hypothesis test.

(2 pts.) c) Calculate and interpret the appropriate confidence interval or bound. (1 pt.) d) In practical terms, does the data imply that the true mean speed is more for the 15 inch

mound vs the 10 inch mound? This part uses the information from parts b) and c). If no addition reasoning is provided, you will receive 0 points. The precision of the recording device is 1 mph.

(1 pt. BONUS) e) Explain why the results in parts b) and c) are consistent with each other. (10 pts.) 2. The time it takes for general anesthesia to work (time to induction) is an important

consideration during an emergency and for scheduled surgeries. Note that this the time that it takes for the anesthesia to have an effect at the beginning of the surgery; more anesthesia may have to be administered during the surgery. Recently, a study was conducted to compare the mean induction time of similar drugs when administered via inhalation versus intravenously. Random samples of patients requiring general anesthesia were obtained, and the induction times (in minutes) were measured. Please assume that the distribution is normal. The summary data are given in the following table.

Measure n x̄ s

Induction time for Inhalation 44 3.55 0.280

Induction time for Intravenous 44 3.40 0.374

Difference in Induction Time (Inhalation – Intravenous) 44 0.15 0.315

(1 pt.) a) Should this situation be analyzed via a 2-sample independent or paired method?

Please explain your answer. (6 pts.) b) Is there any evidence to suggest that the mean time to induction for the two methods

is different? Use = 0.05. Remember to include the complete 4-step method in the hypothesis test.

(2 pts.) c) Calculate and interpret the appropriate confidence interval or bound.

STAT 350 (Spring 2017) Homework 9 (20 points + 1 point BONUS) 2

(1 pt.) d) In practical terms, does the data imply that the mean time is different for the two methods? This part uses the information from parts b) and c), however, if no addition reasoning is provided, you will receive 0 points. The precision of the recording device is 0.1 minutes.

Additional Problems: 10.15, 10.17, 10.19, 10.21, 10.23, 10.53, 10.73, 10.79