IMathAS-libretexts

5. We are considering two variables: the level of the child's family income as low or high, and the classification for the size of coin the child drew as too small or too large. Are these two categorical variables related? Conduct a chi-square test for Independence to see whether the variables are related. Test at the 0.05 significance level.

a) Identify the correct alternative hypothesis for this test.

There is no relationship between family income level and coin size classification.
There is a relationship between family income level and coin size classification.
Family income level and coin size classification are independent.
Family income level varies much more than coin size.

b) The

\displaystyle \chi^{{2}}

test statistic value is:

c) The P-value is:

d) Based on this, we

Reject $\displaystyle {H}_{{0}}$
Do not reject $\displaystyle {H}_{{0}}$

e) Which means

The data is not strong enough to support that there is a significant relationship between the two variables.
There is a significant relationship between the two variables.
There is definitely no relationship between the two variables.
The two variables are mutually exclusive.

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