Question

In Exercises 7.1 to \(7.4,\) find the expected counts in each category using the given sample size and null hypothesis. $$ \begin{aligned} &\mathbf{7 . 3} \quad H_{0}: p_{A}=0.50, p_{B}=0.25, p_{C}=0.25 ;\\\ &n=200 \end{aligned} $$

Short answer

The expected counts for categories A, B, and C are 100, 50, and 50, respectively.

Step-by-step solution

Find Expected Count for Category A

To find out the expected count for category A, multiply its proportion given by the null hypothesis (\(p_A=0.50\)) by the total size of the sample (\(n=200\)). Therefore, the expected count for category A is \(n*p_A = 200*0.50 = 100\)

Find Expected Count for Category B

To get the expected count for category B, multiply its proportion given by the null hypothesis (\(p_B=0.25\)) by the total size of the sample (\(n=200\)). Therefore, the expected count for category B is \(n*p_B = 200*0.25 = 50\)

Find Expected Count for Category C

To obtain the expected count for category C, multiply its proportion given by the null hypothesis (\(p_C=0.25\)) by the total size of the sample (\(n=200\)). Therefore, the expected count for category C is \(n*p_C = 200*0.25 = 50\)