Answer: 0.1010052
Step-by-step explanation:
Given : Significance level : [tex]\alpha=0.01[/tex]
Alternative hypothesis : [tex]H_1:\ p\neq\dfrac{3}{4}[/tex]
The test statistic value : [tex]z=-1.64[/tex]
Since , the alternative hypothesis is two-tailed, so the test is a two-tailed test.
Using standard normal distribution table for z, we have
The P-value of two-tailed test will be :-
[tex]2P(z>|-1.64|)=2P(z>1.64)\\\\=2(1-P(z\leq1.64))\\\\=2(1-0.9494974)\\\\=0.1010052[/tex]
Hence, the P-value = 0.1010052
