Howdy! I'm professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to find and interpret the probability of flu side effects from a cholesterol treatment. Here's our problem statement: The probability of flu symptoms for a person not receiving any treatment is 2%. In a clinical trial of a common drug used the lower cholesterol, 19 of 840 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 19 people experienced flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug?
OK, Part A of this problem asks us for the probability that at least 19 people from our sample experienced flu symptoms. Now, normally --- pun intended --- we would use a normal distribution to solve a problem like this. But notice in the problem statement, we don't get any information about a mean or a standard deviation for our distribution. So what information are we given? Well, we're given this information here: a probability of "success" and then we're given here a proportion of our sample. So what we're going to do with this information then is use the binomial distribution as an approximation for the normal.
To start out with, we're going to have to load up StatCrunch. So let's open that up here, and I'll pop this window out. And let's move this around so we can see everything quite a bit better. OK, so now here in StatCrunch, we're going to go to Stat --> Calculators --> Binomial. Here in my binomial calculator, I need to insert the sample size. That's n, so my sample size here is the total number of people in the sample, which is the 840. p is the probability of success, which we saw earlier in our problem statement is 2%. And then I want the probability that x is going to be greater than or equal to 19 --- greater than or equal to 19. And there's my probability. I'm asked to round to four decimal places. Fantastic!
Now Part B of this problem asks, "What does the result from Part A suggest?" OK, this one is a little tricky for a lot of students, and I admit it's a little tricky for me too because sometimes the logic that the statisticians use makes you feel like you're wrapping your brain around a tree. But let's go through each one of these answer options one at a time and see what we can make of this.
Answer option A says, "The drug has no effect of flu symptoms because x greater than or equal to 19 is highly unlikely." Well, the drug doesn't have an effect on flu symptoms. That part is true, because remember we did this probability distribution on the assumption that the drug has no effect on the likelihood of flu symptoms. So that's our assumption. So to be true with that assumption, we're going to have to suggest that that's what our results going to suggest, that the drug has no effect on flu symptoms. But looking at the probability here, I mean you've got almost a one in three chance. And I would feel more comfortable if the probability were greater than 50% to say that it's, that it's likely or not likely. But you know, one in three chance. Hey, we can consider that to be significant. So highly unlikely? No, we're going to say ... we're going to say that it's likely, not unlikely.
Answer option B says, "The drug increases the likelihood of flu symptoms because x greater than or equal to 19 is not highly unlikely." Well, the drug's not increasing the likelihood of flu symptoms because we're assuming that it doesn't do that. So we're not going to choose Answer option B. Answer options C starts out the same way. "The drug increases the likelihood of flu symptoms." So we're not going to choose that answer.
Answer option D says, "The drug has no effect on flu symptoms because our probability is not highly unlikely." Wow. Yeah. We're really wrapping our brain around a tree here. "Not highly unlikely." Let's get rid of that double negative so we can make more sense of this. We're saying our probability is highly likely. Well, a one in three chance? Yeah, I don't know if I call it highly likely, but given the way some of these statisticians think, yeah, they might be actually considering that highly likely. So let's go ahead and select Answer option D. Excellent!
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Frustrated with a particular MyStatLab/MyMathLab homework problem? No worries! I'm Professor Curtis, and I'm here to help.