Answer:
The null hypothesis is given as
while the alternate hypothesis is 
Step-by-step explanation:
As per the the given data
p1=Proportion of Homeowners who would buy the security system
p2=Proportion of Renters who would buy the security system
As the null hypothesis states that there is no difference in the test thus it is given as

This states that there is no difference between the probabilities of the homeowners buying the security system and the renters buying the security system.
The Alternative hypothesis is the other possibility of the null hypothesis. i.e It negates the null Hypothesis and is given as

The correct answer would in fact be 52
we are given

step-1: Simplify expression inside parenthesis
we will combine like terms
so, firstly we will take common denominator



step-2: Distribute 1/2 inside


step-3: Combine like terms

We can find common denominator




we can also write it as in mixed form

so, we will get

option-C.............Answer