Answer:
You can decide to <u>reject</u> the Null Hypothesis at p < 0.05.
Step-by-step 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, <em>r</em> = 2.
The categories of weight in adulthood are:
Low to normal, Overweight, and Obese
So, number of columns is, <em>c</em> = 3.
The distribution of the statistic
is chi-square with (<em>r </em>- 1)(<em>c </em>- 1) degrees of freedom, where <em>r</em> represents the number of rows in the two-way table and <em>c</em> represents the number of columns.
Compute the degrees of freedom as follows:
![df = (r-1)(c-1)=(2-1) \times (3-1) = 2](https://tex.z-dn.net/?f=df%20%3D%20%28r-1%29%28c-1%29%3D%282-1%29%20%5Ctimes%20%283-1%29%20%3D%202)
It is provided that the calculated value of Chi-square test statistic is 18.26.
Compute the <em>p</em>-value of the test as follows:
![p-value=P(\chi^{2}_{2}\geq 18.26)\\=0.000108\\\approx0.00011](https://tex.z-dn.net/?f=p-value%3DP%28%5Cchi%5E%7B2%7D_%7B2%7D%5Cgeq%2018.26%29%5C%5C%3D0.000108%5C%5C%5Capprox0.00011)
Decision rule:
The null hypothesis will be rejected if the <em>p</em>-value of the test is less than the significance level.
The significance level is, <em>α</em> = 0.05.
<em>p</em>-value = 0.00011 < <em>α</em> = 0.05.
The null hypothesis will be rejected at 5% level of significance.
Thus, the complete statement is:
"You can decide to <u>reject</u> the Null Hypothesis at p < 0.05."