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Five steps to finding your sample size Define population size or number of people. Designate your margin of error. Determine your confidence level. Predict expected variance. Finalize your sample size.
10 Percent Rule: The 10 percent rule is used to approximate the independence of trials where sampling is taken without replacement. If the sample size is less than 10% of the population size, then the trials can be treated as if they are independent, even if they are not.
Normal: The sampling distribution of (the sample mean) needs to be approximately normal. This is true if our parent population is normal or if our sample is reasonably large ( n 30 ) . Independent: Individual observations need to be independent.
Assumptions Behind the Central Limit Theorem The data must follow the randomization condition. It must be sampled randomly. Samples should be independent of each other. Sample size should be not more than 10% of the population when sampling is done without replacement. The sample size should be sufficiently large.
Key Takeaways. The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the populations distribution. A sufficiently large sample size can predict the characteristics of a population more accurately.
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Two-sample t-test assumptions Data values must be independent. Measurements for one observation do not affect measurements for any other observation. Data in each group must be obtained via a random sample from the population. Data in each group are normally distributed.
The conditions we need for inference on a mean are: Random: A random sample or randomized experiment should be used to obtain the data. Normal: The sampling distribution of (the sample mean) needs to be approximately normal.

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