Question

A student wants to survey the sophomore class of 200 students about whether the school should require uniforms. A random sample of 18 sophomores is surveyed and asked whether they support the school adopting uniforms, and three students said yes. The student wants to construct a 95% confidence interval for the proportion of sophomores who favored the adoption of uniforms. Are the conditions for inference met

Answer 1

Answer:

Option D

Step-by-step explanation:

Complete question

A student wants to survey the sophomore class of 200 students about whether the school should require uniforms. A random sample of 18 sophomores is surveyed and asked whether they support the school adopting uniforms, and three students said yes. The student wants to construct a 95% confidence interval for the proportion of sophomores who favor the adoption of uniforms. Are the conditions for inference met?

1. Yes, the conditions for inference are met.
2. No, the 10% condition is not met.  
3. No, the randomness condition is not met.  
4. No, the Large Counts Condition is not met.

Solution

10 % of population size of 200 is 20. The sample of 18 is smaller than the 10 % of sample size of 200. As per the 10% rule, the size of sample must be less than 10% of the total size of population. This indicate that the sample is random but its size is less that 30. However, it should be greater that 30. Hence, the large count condition is not met.

Hence, option D is the correct choice of answer