# For the following experiment, state the type of test we should use. Assume homog

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
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Step 1
Given:
The assumptions that can be made are:
1) Homogeneity of variances.
2) Validity of parametric test.
3) The size of the sample(n) is large.
4) The population standard deviation is unknown.
Explanation of incorrect options:
In general, a t-test and a z-test can not be performed for the given study as both these tests are used for comparing the means of the two populations, and in the given scenario, the data is based on the counts and the options available for the children.
Therefore, a t-test or a z-test of any kind like two-sample (heterogeneity and homogeneity), one sample cannot be performed.
Step 2
The test that will be performed is a "Chi-squared goodness of fit test".
In the given scenario, the variable in the given study is categorical, and the data is based on the preference of children for a certain type of toy; this means there is a goodness of fit that is to be tested.
Therefore, it is the only test from the given options that will be used for the given study.
Hence, the correct option is:
chi-squared goodness of fit.