Question 4 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A manufacturing company packages shipments in either large or small boxes. A random sample of 40 shipments that are packaged in large boxes is found to have a mean of 15 pounds and a standard deviation of 2.8 pounds. A separate random sample of 50 shipments that are packaged in small boxes is found to have a mean of 10 pounds and a standard deviation of 1.5 pounds. The manager would like to know if the data provide convincing evidence that the true mean weight of all shipments that are packaged in small boxes is less than the true mean weight of all shipments that are packaged in large boxes. The manager tests H0: μS – μL = 0, Ha: μS – μL < 0, where μL = the true mean weight of all shipments that are packaged in large boxes and μS = the true mean weight of all shipments that are packaged in small boxes. The conditions for inference have been met. The standardized test statistic is t = –10.19 and the P-value is less than 0.0005. What conclusion should be made using the significance level = 0.01?
Answer
A
Reject H0. There is convincing evidence that the true mean weight of all shipments packaged in small boxes is less than the true mean weight of all shipments packaged in large boxes.
B
Reject H0. There is not convincing evidence that the true mean weight of all shipments packaged in small boxes is less than the true mean weight of all shipments packaged in large boxes.
C
Fail to reject H0. There is convincing evidence that the true mean weight of all shipments packaged in small boxes is less than the true mean weight of all shipments packaged in large boxes.
D
Fail to reject H0. There is not convincing evidence that the true mean weight of all shipments packaged in small boxes is less than the true mean weight of all shipments packaged in large boxes.