The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students’ attitudes toward school and study habits. Scores range from 0 to 200. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to an SRS of 45 of the over 1000 students at her college who are at least 30 years of age. Check the conditions for carrying out a significance test of the teacher’s suspicion.

The distribution of frequencies of all possible results for a statistic of a population parameter refers to the sampling distribution of a given population.

According to the central limit theorem, whenever the sample size is greater than 30, the sample mean distribution follows a normal distribution. In addition to this, the sample size should be less than $10\%$of the actual population.

It can be observed that the sample size given is equal to 45, that is, satisfies the normality condition.

Thus, the condition should be applied while choosing a simple random sample and satisfies the following condition:

1. The sample size should be atleast 30.

2. The population size must be greater than the sample size.

3. The sample size should be atleast greater than 10% of the actual population.