Question

Both cats and dogs hunt small mammals. Biologists will randomly select 20 dogs and 20 cats living in northern England and attach video cameras to their collars. The biologists then observe how many small mammals each animal kills during a ten-day period. They plan to choose the dogs independently of the cats, and hope to come as close as possible to using simple random sampling, so they can use a test of two means with independent samples to determine whether cats kill more small mammals than dogs. Their hypotheses are H0:μcats=μdogs and Ha:μcats>μdogs . Are the requirements for the hypothesis test of this question satisfied? Explain.

Yes. Independent simple random samples are all that is required.

Yes. They will have 40 subjects in all, which is more than 30.

No. They must have at least 30 cats and at least 30 dogs.

Not necessarily. Because they will only have 20 subjects in each sample, the data for each sample will have to be normal.

Answer 1

let be the true mean number of small mammals killed by the cats and be the true mean number of small animals killed by the dogs. The biologists want to determine whether cats kill more small mammals than dogs, that is if . This will be the alternative hypothesis.

The hypotheses are

Since the the dogs are chosen independently of the cats, using simple random sampling, the test of two means with independent samples to determine whether cats kill more small mammals than dogs can be used.

But the sample sizes of each of the sample of dogs and cats is less than 30 and we do not know the population standard deviations of number of small mammals killed by cats and dogs.

Hence we cannot test the difference in means using normal distribution.

Then to test the difference in means using t distribution, we need the data for each sample to be normal or approximately normal. Since this information is not provided, we will pick

ans:  Not necessarily. Because they will only have 20 subjects in each sample, the data for each sample will have to be normal.