For the following experiment, state the type of test we should use. Assume homogeneity of variance (where applicable), unless something is directly stated (e.g., "the data are not at all normal") or otherwise indicated (viz., by the inspection of the data) which would indicate an obvious violation of an assumption. This means you must inspect the data for violations of all assumptions. Assume n is large enough, unless stated. Assume $\sigma$ is unknown, unless stated.

Brianna works at an infant/toddler center and wants to know whether children at the age of two have a preference for a certain type of toy. She puts four different toys in front of the infant/toddler and sees which toy the child crawls to first.

1) a one-sample t-test for means

2) none of the other tests

3) an independent samples t-test with heterogeneity of variance

4) a related samples t-test

5) and independent samples t-test with homogeneity of variance

6) a chi-squared goodness-of-fit test

7) a z-test for the difference between proportions

8) a one sample z-test for proportions

9) a one-sample z test for means

Brianna works at an infant/toddler center and wants to know whether children at the age of two have a preference for a certain type of toy. She puts four different toys in front of the infant/toddler and sees which toy the child crawls to first.

1) a one-sample t-test for means

2) none of the other tests

3) an independent samples t-test with heterogeneity of variance

4) a related samples t-test

5) and independent samples t-test with homogeneity of variance

6) a chi-squared goodness-of-fit test

7) a z-test for the difference between proportions

8) a one sample z-test for proportions

9) a one-sample z test for means