Question 1
Conducting a completely randomized survey of 100 Montgomery County, Tennessee residents. Since simple random sampling assumes that the people to be sampled should be from a given list, the people in the population have to be sampled by a random process. In this case, three methods could be used; which are the use of a random number table, manual number selection, or a random number generator. This ensures that every individual remaining in the County’s population gets the same likelihood of being chosen for the 100-names-sample.

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Considering it is not practicable to have a list of all people living in the county, simple random sampling cannot work for this case. As such, the systematic sampling method can be used. This is because it is not only simple but also delivers quality. The population to be sampled can be defined as the Montgomery County Registered Voters. The up-to-date list of the voters from this county can be obtained from the relevant authorities and used for the survey. The researcher in this case then randomly picks the first subject from the given list and continues to pick every nth person from that list.

The procedure, in this case, happens by manually picking the starting number that should be an integer. The chosen integer corresponds to the initial subject for the 100-individual-sample from the County. With over 62,000 registered voters, the interval to cover in order to select 100 individuals from the list is 620. Assuming the first subject is the 15th on the list, the next subject would be the 635th on the list. This continues until all the 100 individuals are chosen. Since there’s even sampling, there is assurance that the chosen 100-individual-sample not only represents the entire population, but also eliminates clustered picking of subjects. A team of researchers can then proceed and schedule meetings with the chosen 100 individuals in the sample list to be surveyed, and the data analyzed and conclusions made.

Information collected and obtained from a sample such as this one will definitely be representative of the entire population.

Question 2
If 55% taking tests are pregnant and tests accurately indicate pregnancy 99% of the time and non-pregnancy 99.2% of the time, what is the probability someone who gets a positive reading is pregnant?

Given that 55% of those who take tests are pregnant, the probability, of selecting a pregnant person, is 55/100. The probability that a personality who receives a positive reading is actually pregnant then depends on the accuracy of the tests that are done. In this case, for this reason, tests normally indicate pregnancy 99% of the time which translates to 99/100.

The probability that a woman selected from those taking tests getting a positive reading and actually being pregnant then comes to:
55/100 x 99/100
Which equals:
0.55 x 0.99
=0.5445
=54.45%.

This probability is an indication that the tests are highly accurate, and the likelihood, of getting the wrong reading, is very low. Assuming that a woman gets a positive reading but is not actually pregnant, the probability would be:
0.55 x 0.01
Which equals:
0.0055 = 0.55%
This is a representation of less than 1% of the entire population of those who get tested for pregnancy.

The calculation of the probability in the case above can be represented as:
Probability, of 55% taking tests being pregnant, can be P (A)
Probability of a test indicating pregnancy = 99% = P (B)
Probability of someone who gets a positive reading is pregnant = P (A) and P (B)
This translates to P (A) x P (B):
P (A) * P (B)