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Question

It is claimed that 75% of puppies are house-trained by the time they are 6 months old. To investigate this claim, a random sample of 50 puppies is selected. It is discovered that 42 are house-trained by the time they are 6 months old. A trainer would like to know if the data provide convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. Are the conditions for inference met?

A. Yes, the conditions for inference are met.

B. No, one condition is not met.

C. No, two conditions are not met.

D. No, three conditions are not met.

Answer 1

The conditions for inference in this scenario are:

1. Random Sample: The sample of 50 puppies should be randomly selected from the population of interest.
2. Independence: The puppies in the sample should be independent of each other.
3. Sample size: Both np and n(1-p) should be greater than or equal to 10, where n is the sample size and p is the hypothesized proportion of house-trained puppies.

In this scenario, we are not given information about how the sample of puppies was selected. Assuming the sample is random, we can assume that the first condition is met.

We are not given any information about whether the puppies in the sample are independent of each other, but it is reasonable to assume that this condition is met.

The sample size is n=50, and the hypothesized proportion is p=0.75. The expected counts for the two categories (house-trained and not house-trained) are np = 50 x 0.75 = 37.5 and n(1-p) = 50 x 0.25 = 12.5. Both of these expected counts are greater than or equal to 10, so the sample size condition is also met.

Therefore, the conditions for inference are met, and the correct answer is A: Yes, the conditions for inference are met.