Answer:
The value of the test statistic is -0.4.
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 0.25[/tex]
The alternate hypotesis is:
[tex]H_{1} \neq 0.25[/tex]
We have to find the standard deviation [tex]\sigma[/tex], which is
[tex]\sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]
In which p is the proportion estimated at the null hypothesis.
Sample of 540. So
[tex]\sigma = \sqrt{\frac{0.25*0.75}{540}} = 0.0186[/tex]
Our test statistic is:
[tex]t = \frac{X - p}{\sigma}[/tex]
In which X is the mean calculated.
So
[tex]X = \frac{104}{540} = 0.1926[/tex]
[tex]t = \frac{X - p}{\sigma}[/tex]
[tex]t = \frac{0.1926 - 0.2}{0.0186}[/tex]
[tex]t = -0.4[/tex]
The value of the test statistic is -0.4.
