Let p be the population proportion of the drivers using cell phones while driving.
Given : A police officer claims the proportion of drivers using cell phones while driving 35%.
i.e. [tex]p=0.35[/tex]
To test this claim, a random sample of drivers are monitored and checked if are using a cell phone while driving.
Then, the appropriate hypothesis would be :-
[tex]H_0: p=0.35\\\\ H_a:p\neq0.35[/tex]
∵ Alternative hypothesis is two-tailed , so the test is a two-tailed test.
Also, it is given that the test statistic for this hypothesis test is −2.48.
[tex]z_{calc}=-2.48[/tex]
Since this is a two tailed hypothesis test, assume that the critical values for this hypothesis test are −2.576 and 2.576.
Here, -2.576< -2.48< 2.576
[tex]\Rightarrow\-2.576< z_{calc}< 2.576[/tex]
So we failed to reject the null hypothesis [tex]H_0[/tex] .
Interpretation: We have sufficient evidence to support the claim that proportion of drivers using cell phones while driving 35%.
