It is apt that use of binomial distributions on probability has sundry applications. They can be used in Businesses, Engineering mechanics, Marketing institutions, and other fields such as in Governmental Organizations. Determining if one brand of a product is preferred than the other, is an aspect of hypothesis testing. A hypothesis can be defined as a guess, which the claim is interested in proofing as either true or false.
In this essay discussion, a hypothesis test will be carried out using statistical means, and other methods to either support the claim or decline it. There are two ways of presenting a hypothesis. One is using a null hypothesis, and the other is using an alternative hypothesis. The null plus alternative hypothesis for this question can be presented as follows:
H0: µ=0 Meaning that 40% of toothpaste buyers prefers using Brand A to B
Ha: µ≠0 Meaning that 40% of toothpaste buyers do not prefer Brand A to B
Questions
- How would you do a sample survey?
A sample survey can be carried out by picking up a representative samples of people from each group to ask the questions about the use of toothpaste. After that, the records are taken and then analyzed. This can be completed by giving them the questionnaires or interviewing the users of toothpaste.
- The ethical concern behind only surveying employees of the Manufacturer is that the survey is biased. Some of the employees working for that company may not disclose their information as may be use of toothpaste does ogre them to their society, and through this, it will be a social effect to them.
- The outcomes from the survey can be analyzed using statistical means to determine whether the claim presented is viable or not. If the claim is true, then we accept the null hypothesis and conclude that 40% of the users prefer Brand A to B. On the other hand, if the claim is not be supported by the results then alternative hypothesis is not accepted.
- After a survey was conducted, and they found that 35/100 preferred Brand A, then the claim is true since our estimation is less than the 40% shown in the null hypothesis.
If a random survey had 100 people, then n=100, p=0.35 and 1- Ṕ= 0.65, thus ơ=np(1-p)
Ơ=100*0.35*0.65 = 4.770, then z= 35-404.770 =-54.770 = -1.048, we do not accept the null hypothesis and hence the claim may not be true.
Using 25 people, then Ơ=100*0.25*0.75 =4.3301, and the z= z= 25-404.330 =-154.330 = -3.4640.
The null would not be supported to run the ad based on the negative results obtained. The justification of the running ad would be justified if, the number of respondents who would be found preferring Brand A to B were many. That means it would increase the chances of liking brand A. this can be done by increasing the scope of the survey, and may be include more people to be interviewed or asked to fill in the questionnaires.
