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

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 \( N \) must be at least:

\[
N \geq \frac{35}{0.10} = 350
\]

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

The correct answer is:

**A.) 350**

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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.

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

In this problem, we explore the minimum population size required to treat a sample of 35 students as independent when sampling without replacement. This involves the 10% rule, ensuring that the sample size is small enough relative to the population. Suitable for students in Grades 10-12.

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