# Tutor profile: Vikas R.

## Questions

### Subject: Public Health

Suppose that there are are 10,000 people in the fictional village of VillageVille. Now, a recent outbreak of tuberculosis just occurred in which 35 residents showed signs of the disease in the past week. Before this outbreak, there were already 15 previous residents who had tuberculosis and still continue to present these symptoms. What can we say is the prevalence rate of tuberculosis in VillageVille?

First, we need to understand what prevalence is and what is the formula for prevalence rate. Prevalence is the proportion of a population or community who have the disease at given time period or at a point in time. There are variations of the prevalence equation but in this example let's use the formula: prevalence = (new and existing cases of disease at a point in time) / (total population during or at that time). In this example, the numerator is 35 + 15 = 50 because there are 35 new cases of tuberculosis and 15 pre-existing cases of tuberculosis. The denominator is 10,000 since that is the population at that time. Thus, our simplified equation is 50/10,000 = 0.005 or 5 per 1,000. So, our prevalence rate of tuberculosis in VillageVille is 5 cases of tuberculosis per 1,000 residents.

### Subject: Statistics

Suppose we are trying to test a claim that a medication called MysteryPill causes a difference in the rate of cancer in the general public (ex: 5.5%) . If we are testing with a significance level of 0.05 and our test returns a p-value of 0.07, should we reject or fail to reject our null hypothesis and what should our conclusion say?

So in this example it is important to first understand what our hypothesis could like. Our null hypothesis would state that there isn't a difference that our test seeks to claim and our alternative hypothesis would be that there is an observed difference that the test wants to prove. For example, we could write this as H0: MysteryPill does not cause a difference in the 5.5% rate of cancer in the public, HA: MysteryPill causes a difference either less than or greater than the 5.5% rate of cancer in the public. Now, since our significance level can also be called "alpha" and it is equal to 0.05 or 5%. Our p-value is what we observed which means that there is a probability of 0.07 or 7% of observing a sample statistic that is at least as extreme as observed under the null hypothesis (H0). Since our p-value of 0.07 is greater than the significance level (0.07 > 0.05), we fail to reject the null hypothesis and conclude that there is no observed difference in the rate of cancer of 5.5% in the general public with the use of MysteryPill.

### Subject: Algebra

There are two numbers whose combined sum is equal to 19. One of these numbers is greater than the other number by 3. What are these two numbers?

This type of question involves solving an equation for a variable. In this specific instance, we want to find out what the two numbers are. Let's label "X" as our largest number. Also, "X" can be any number we set it equal too but in this example X is the higher value number. Now we focus on the smaller number which is 3 less than the larger number. So this number will be "X-3". Next, we can know that the sum of the larger and smaller number shown as "X" and "X-3" = 19. So we can set the equation up as X + X - 3 = 19. First, let's add 3 to both side so that we have our x variable on one side. This simplifies to 2X = 22. Next, we can solve for X by dividing both sides by 2 to get X = 11. Since X = 11 we know our larger number is 11 and to get our smaller number we solve X - 3 to get 11 - 3 = 8. Thus, our two numbers are 8 and 11. We can also check this because we know that the sum of those 2 numbers is 19 and 8+11 = 19.

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