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Chapter 6: Q2 (page 272)

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.

Short Answer

Expert verified

It is incorrect to conclude that the sample means cannot be treated as values from a normal distribution as the sample size is too small because it is mentioned that the population of weights of golden retriever dogs is normally distributed.

Thus, all samples selected from this population will be normally distributed.

Step by step solution

01

Given information

It is given that weights of golden retriever dogs are normally distributed and samples of size equal to 15 are extracted from this population.

02

Requirements under which sample means is said to follow a normal distribution

One of the following requirements must be fulfilled for the computed sample mean to be treated as a value from a normally distributed population.

  • It should be clearly stated that the sample is extracted from the normally distributed population.
  • The sample size should be greater than 30.

Here, it is given that the population of weights of golden retriever dogs is normally distributed. That is, one of the requirements is met.

Thus, the sample means can be treated as being from a normal population as all the samples will be normally distributed.

It is incorrect to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small.

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