In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a research proposa
l in which a telephone company wants to determine whether the appeal of a new security system varies between homeowners and renters. Independent samples of 140 homeowners and 60 renters are randomly selected. Each respondent views a TV pilot in which a test ad for the new security system is embedded twice. Afterward, each respondent is interviewed to find out whether he or she would purchase the security system. Results show that 25 out of the 140 homeowners definitely would buy the security system, while 9 out of the 60 renters definitely would buy the system. (a) Letting p1 be the proportion of homeowners who would buy the security system, and letting p2 be the proportion of renters who would buy the security system, set up the null and alternative hypotheses needed to determine whether the proportion of homeowners who would buy the security system differs from the proportion of renters who would buy the security system.
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
We can have a schematic view of a diagrammatic illustration in our mind where the distance of the pool to Lincy is (20 + r ) and the distance to the tangent is 49.
So; by using pythagoras theorem, since the radius meets the tangent at a right angle; we have:
