# How do you create statistical hypotheses for an ANOVA test?

## To investigate maternal behavior of laboratory rats Bob separated the rat pup from the mother and recorded the time in seconds required for the mother to retrieve the pup. He ran the study with 5, 20, and 35 day old rat pups because he was interested in whether retrieval time varies with age of the pup. The data are given below, where there are six pups per group. Using a .05 significance level, determine if there is a significant difference between the groups. a. state the statistical hypotheses b. the decision rules c. construct a summary table d. indicate your calculated value and interpret the results e. what proportion of variance in the time to retrieve the rat pups can be accounted for by age? 5 Days Old: 15, 10, 25, 15, 20, 18 20 Days Old: 30, 15, 20, 25, 23, 20 35 Days Old: 40, 35, 50, 43, 45 40

##### 1 Answer
Jun 21, 2018

You already clearly stated that what you want to know is whether retrieval time varies with age of the pup. That's what the hypotheses are all about.

#### Explanation:

There are two statistical hypotheses, namely the null and the alternative. The null is the one you would like to reject. In this case, you would like to reject the hypothesis that 'there is no difference in the retrieval time among the 3 age groups'.

If you reject the null, you end up with the alternative, which is 'the retrieval time of at least one of the 3 groups differs from the others'.

In the more common form, the two hypotheses are something like the followings:

$H o$ : No difference in retrieval time among the 3 age groups.
$H a$ : At least one of the age groups indicates a different retrieval time.