BHS 220 Module 3 Case 3 Introduction to Hypothesis Testing

Trident University International

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Module 3 Case Assignment – Introduction to Hypothesis Testing

BHS220 – Introduction to Health Statistics

Session – APR2017FT-1

Dr. SharleneGozalians

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Assignment instructions:

Discuss probability. What is its history? What is the theory of probability? How is it calculated? What are the advantages and disadvantages of using this technique?

Identify and discuss the two major categories of probability interpretations, whose adherents possess conflicting views about the fundamental nature of probability.

Based on this survey, what is the probability that a randomly selected American adult has never been tested? Show your work. Hint: using the data in the two total rows, this would be calculated as p (NT) / (p (NT) + p (T)), where p is probability.

What proportion of 18- to 44-year-old Americans have never been tested for HIV? Hint: using the values in the 18–44 cells, this would be calculated as p (NT) / (p (NT) + p (T)), where p is probability. Show your work.

Probability

Probability can be defined as the chance that something or some event will happen out of the number of possible outcomes. The example of the prediction of the chance of snow in the winter is an instance of probability. Forecasters usually give a range from zero to 100% chance of snow for a given geographical area within a designated time period. We use these forecast to determine if it will or will not snow and when.

The history probability was said to have begun with the correspondence between Blaise Pascal and Pierre de Fermat in 1654. This conclusion is stated as incorrect because the origins of probability started centuries before with lay people and mathematicians. The true beginning of probability is difficult to trace because it began as empirical science and much later developed into mathematical science (Lightner, 1991). The correspondence between Pascal and Fermat was in reference to the game of chance where a pair of dice was to be thrown 24 times and to decide whether or not to bet even money on the chance that at least one of the 24 times the dice would land on double six to increase the chase of winning., this gave way to the fundamental principles of probability.

“Probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance “(Siegmund, 2005).

Probability is calculated defining the number of events divided by the number of possible outcomes. For example, a cookie jar contains 4 chocolate chip, 5 oatmeal and 11 peanut butter cookies. If a cookie is pulled from the cookie jar at random, what is the probability the cookie is oatmeal? In the example, choosing an oatmeal cookie is the event, and the number of outcomes is the total number of cookies in the jar, which are 20.So probability would be calculated by dividing the number of oatmeal cookies by the total number of cookies in the jar. Then you would multiply that number 100 to make it a percent. See the below equation (single random event):

P = 5/20 = 0.25 or 25%

The advantages of using probability in random sample is having a better chance the sample represents the entire population, lesser time to be conclude, cost effective, lesser degree of judgement required, simplistic sampling, and you don’t have to be a mathematician to do it. The disadvantages include limiting sample selection to a few variations and sampling can become redundant and monotonous (Devkota, 2017).

Major Categories of Probability

The two major categories of probability interpretations are objective and subjective. Objective probability is a probability that an event will occur which is based on investigation in which each measure is based on a recorded observation, rather than a subjective estimate (Investopedia, 2016). An example of objective probability is tossing a coin in the air 100 times and recording how many times it landed on heads. Subjective probability is a probability garnered from an individual’s personal judgment about whether a specific outcome is likely to occur (Investopedia, 2016). An example of subjective probability would be watching individuals at a basketball game and estimating who will win the game. After all of the variables are gathered, the administrator can provide the final probability.

Survey Results

Based on the survey, the probability that a randomly selected American adult has never been tested is 63%. See table and work below:

p (134767) divided by p (134767) + p (77789)

p = 134767 / 212556= 0.63 multiplied by 100 = 63%

This means 63% of the population of a random American adult has never been tested.

HIV Proportion

The probability of the age group 18 – 44 year old Americans which have never been tested for HIV is calculated using the total amount of 18 – 44 years old Americans never tested and dividing it by the total number of 18 – 44 years old + the total number of 18 – 44 years old tested.

p (56405) divided by p (56405) + p (50080)

p = 56405 / 106485 = 0.53 multiplied by 100 = 53%

This means that in 53% of the population, 18-44 year old Americans have never been tested for HIV.

References

Devkota , B. R. (2017). Simple Random Sampling, Advantages, Disadvantages. Retrieved May

10, 2017,from https://www.mathstopia.net/sampling/definition-advantages-disadvantages

Investopedia.(2016). Subjective Probability. Retrieved May 15, 2017, from

http://www.investopedia.com/terms/s/subjective_probability.asp

Lightner, J. E. (1991).A Brief Look at the History of Probability and Statistics. National Council

ofTeachers of Mathematics, 84(8), 623-630. Retrieved May 10, 2017, from

https://www.jstor.org/stable/27967334?seq=1#.

Siegmund, D. O. (2005).Probability theory. Encyclopædia Britannica, inc. , 1-11.