Answer: z =2.39
Step-by-step explanation:
Given :
[tex]H_0: p \leq0.23\\\\ H_a: p > 0.23[/tex]
A random sample of 136 households found that 43 consisted of one person.
i.e. Sample size : n= 136
Sample proportion : [tex]\hat{p}=\dfrac{43}{136}=0.316176470588\approx0.3162[/tex]
Test statistic for proportion :-
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]\Rightarrow z=\dfrac{0.3162-0.23}{\sqrt{\dfrac{0.23(1-0.23)}{136}}}\\\\\Rightarrow\ z=\dfrac{0.0862}{\sqrt{0.00130220588235}}\\\\\Rightarrow\ z=\dfrac{0.0862}{0.0360860898734}\\\\=2.38873206552\approx2.39[/tex]
Hence, the value of the test statistic: z =2.39
