Question

You are studying the relationship between the history of early childhood trauma (categorized as trauma/no trauma) and weight in adulthood (categorized as low to normal, overweight, and obese). Past research has suggested that those children who experienced trauma (such as child abuse) are more likely to develop weight problems in adulthood. You calculated a Chi-square of 18.26. You can decide to ____ the Null Hypothesis at p<.05.

Answer 1

You can decide to reject the Null Hypothesis at p < 0.05.

Explanation:

In this case, the relationship between the history of early childhood trauma and weight in adulthood are being studied.

The categories of childhood trauma are:

Trauma and No trauma.

So, number of rows is, r = 2.

The categories of weight in adulthood are:

Low to normal, Overweight, and Obese

So, number of columns is, c = 3.

The distribution of the statistic
`\chi^(2)` is chi-square with (r - 1)(c - 1) degrees of freedom, where r represents the number of rows in the two-way table and c represents the number of columns.

Compute the degrees of freedom as follows:

`df = (r-1)(c-1)=(2-1) * (3-1) = 2`

It is provided that the calculated value of Chi-square test statistic is 18.26.

Compute the p-value of the test as follows:

`p-value=P(\chi^(2)_(2)\geq 18.26)\\=0.000108\\\approx0.00011`

Decision rule:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

The significance level is, α = 0.05.

p-value = 0.00011 < α = 0.05.

The null hypothesis will be rejected at 5% level of significance.

Thus, the complete statement is:

"You can decide to reject the Null Hypothesis at p < 0.05."