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StatisticsQ&A LibrarySmall Sample Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size n = 15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain.Question

Asked Jan 27, 2020

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Small Sample Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size n = 15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain.

Step 1

**Sampling distribution of the sample mean:**

- If the true population distribution of a random variable, say,
*x*, is normal with parameters, mean*μ*and standard deviation*σ*, then, whatever be the size (*n*) of the sample taken from the population, the distribution of the sample mean is also normal, with parameters, mean*μ*and standard deviation*σ/√n*. - Even if the true population distribution of a random variable, say,
*x*, is not normal and has population mean*μ*, standard deviation*σ*, then, for a large size (*n*≥ 30) of a sample taken from the population, the di...

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