Probability And Inferential Statistics

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1. A patient is classified as having gestational diabetes if their glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca’s doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca’s measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ= 140+X mg/dl and σ = X+1 mg/dl, where X is the last digit of your GCU student ID number. What is the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:

Once?
X+1 times, where X is the last digit of your student ID?
X+4 times, where X is the last digit of your student ID?
Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.

2. Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 9X percent reliable, gestational diabetes affects X+1 percent of the population in our patient’s age group, and that our test has a false positive rate of X+4 percent. Compute the following quantities based on this new information:

If 100,000 people take the blood test, how many people that test positive will actually have gestational diabetes?
What is the probability of having the disease given that you test positive?
If 100,000 people take the blood test, how many people that test negative despite actually having gestational diabetes?
What is the probability of having the disease given that you tested negative?
Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?
3. As we have seen in class, hypothesis testing and confidence intervals are the most common inferential tools used in statistics. Imagine that you have been tasked with designing an experiment to determine reliably if a patient should be diagnosed with diabetes based on their blood test results. Create a short outline of your experiment, including all of the following:

A detailed discussion of your experimental design.
How is randomization used in your sampling or assignment strategy?
The type of inferential test utilized in your experiment.
A formal statement of the null and alternative hypothesis for your test.
A confidence interval for estimating the parameter in your test.
An interpretation of your p-value and confidence interval, including what they mean in context of your experimental design

 

 

Sample Solution

ho are involved directly or indirectly with the war and it is lawful to kill ‘to shelter the innocent from harm…punish evildoers (Begby et al (2006b), Page 290).However, as mentioned above civilian cannot be harmed, showing combatants as the only legitimate targets, another condition of jus in bello, as ‘we may not use the sword against those who have not harmed us (Begby et al (2006b), Page 314).’ In addition, Frowe suggested combatants must be identified as combatants, to avoid the presence of guerrilla warfare which can end up in a higher death count, for example, the Vietnam War. Moreover, he argued they must be part of the army, bear arms and apply to the rules of jus in bello. (Frowe (2011), Page 101-3). This suggests Frowe seeks a fair, just war between two participants avoiding non-combatant deaths, but wouldn’t this lead to higher death rate for combatants, as both sides have relatively equal chance to win since both use similar tactics? Nevertheless, arguably Frowe will argue that combatant can lawfully kill each other, showing this is just, which is also supported by Vittola, who states: ‘it is lawful to draw the sword and use it against malefactors (Begby et al (2006b), Page 309).’ In addition, Vittola expresses the extent of military tactics used, but never reaches a conclusion whether it’s lawful or not to proceed these actions, as he constantly found a middle ground, where it can be lawful to do such things but never always (Begby et al (2006b), Page 326-31). This is supported by Frowe, who measures the legitimate tactics according to proportionality and military necessity. It depends on the magnitude of how much damage done to one another, in order to judge the actions after a war. For example, one cannot simply nuke the terrorist groups throughout the middle-east, because it is not only proportional, it will damage the whole population, an unintended consequence. More importantly, the soldiers must have the right intention in what they are going to achieve, sacrificing the costs to their actions. For example: if soldiers want to execute all prisoners of war, they must do it for the right intention and for a just cause, proportional to the harm done to them. This is supported by Vittola: ‘not always lawful to execute all combatants…we must take account… scale of the injury inflicted by the enemy.’ This is further supported by Frowe approach, which is a lot more moral than Vittola’s view but implies the same agendas: ‘can’t be punished simply for fighting.’ This means one cannot simply punish another because they have been a combatant. They must be treated as humanely as possible. However, the situation is escala

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