Question

Nearsightedness: It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.

a) True
b) False
c) Insufficient information
d) Not relevant

Answer 1

The question investigates if the proportion of nearsighted children in a sample supports a general belief of its prevalence. Without a hypothesis test, there's insufficient information to determine if the observed higher sample proportion (10.8%) significantly deviates from the expected 8%.

Step-by-step explanation:

The question asks whether the occurrence of being nearsighted in a random sample of 194 children, where 21 are identified as nearsighted, supports the belief that nearsightedness affects about 8% of all children. The sample proportion of 21 out of 194 is approximately 10.8%, which is higher than the stated belief of 8%. However, to determine the correctness of the statement mathematically, one would typically perform a hypothesis test to see if this observed proportion is significantly different from the expected 8%, considering the randomness of sample variation. Without conducting such a test, the provided information alone is insufficient to definitively conclude whether the belief is true or false.