Problem

B. Can we use $t$ procedures to do inference for the mean weight of the population of adult golden retrievers? Explain, and include a sketch of a data plot. (6 points)

Solution

Step 1 :Discuss the assumptions for using a t-test for inference on the mean weight of the population of adult golden retrievers: (1) The sample is random and representative of the population, and (2) The population of weights is normally distributed or the sample size is large enough (usually n > 30) to apply the Central Limit Theorem.

Step 2 :If the sample of golden retrievers is random and representative of the population, and if the population of weights is normally distributed or the sample size is large enough, then we can use t procedures to do inference for the mean weight of the population of adult golden retrievers.

Step 3 :A sketch of a data plot would show a histogram of the sample weights, which should be approximately normally distributed if the assumptions are met.

Step 4 :\(\boxed{\text{Yes, we can use } t \text{ procedures if the assumptions are met.}}\)

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