Math Problem Statement

One condition for performing a hypothesis test is that the observations are independent.

If Jason is sampling 35 students without replacement, the minimum population size would have to be greater than __________ to treat the observations as independent.

A.)

350

B.)

70

C.)

250

D.)

300

Solution

In statistics, a common rule of thumb for treating observations as independent when sampling without replacement is that the sample size should be no more than 10% of the population. This ensures that removing individuals from the population (without replacement) does not significantly alter the population characteristics.

Jason is sampling 35 students, so the population size NN must be at least:

N350.10=350N \geq \frac{35}{0.10} = 350

Thus, the minimum population size must be greater than 350 to treat the observations as independent.

The correct answer is:

A.) 350


Would you like more details or have any questions? Here are five related questions to expand on this topic:

  1. What are other conditions for performing a hypothesis test besides independence?
  2. How does the 10% rule apply to larger or smaller sample sizes?
  3. What is the importance of the Central Limit Theorem in hypothesis testing with small samples?
  4. What happens if the sample size exceeds 10% of the population?
  5. How do we calculate population size if a different percentage rule is used?

Tip: When sampling without replacement, if your sample size exceeds 10% of the population, it's a good idea to adjust for the finite population correction.

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Math Problem Analysis

Mathematical Concepts

Sampling
Probability
Hypothesis Testing

Formulas

Population size ≥ Sample size / 0.10

Theorems

10% Rule in Sampling

Suitable Grade Level

Grades 10-12