Question

The researcher told you that the team had already collected opinions from 20 randomly selected students and found that 55% agreed with the statement. They ask if the sample they obtained is sufficient to estimate the parameter? Explain.

Answer 1

The adequacy of a sample size of 20 students with 55% agreement depends on the confidence level, margin of error, and population variability. Sampling techniques like simple random sampling are used to ensure representativeness. For higher confidence or lower margins of error, larger sample sizes may be required.

Step-by-step explanation:

Whether the sample of 20 students with 55% agreeing to a statement is sufficient to estimate a parameter depends on several factors, including the desired level of confidence, margin of error, and the variability of the population. Sampling is a crucial technique in statistics since it is impractical to survey entire populations. In statistics, random sampling like simple random sampling is often used to minimize bias and ensure that the sample represents the population well.

To determine if a sample size is sufficient, one might use a sample size calculation formula considering confidence level and margin of error. For instance, if we require a 95% confidence level with a 5% margin of error, a larger sample size than 20 might be necessary, like the one mentioned in example 133 where political awareness of students is being surveyed. In cases where extensive time and resources are restricted, such as examining a school's overall GPA or conducting opinion polls, sample sizes might be smaller but should still adequately represent the population.