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a researcher collecting information about 1,000 randomly selected physical therapists concluded that the median hourly wage for physical therapists in the United States at the time of the study was between 22 dollars and 76 cents and fifty-nine dollars twenty four cents with a 95% confidence level which of the following could represent the median hourly wage based on the same sample same sample for physical therapists United States with a 90 percent confidence level so let's just think about what confidence level means that means remember the media is gonna be some number it might be you know the actual median hourly wage for physical therapists might be thirty dollars an hour or twenty-five dollars an hour they're trying to they're trying to they're trying to estimate it by doing this random selection and then they're providing a range and they're saying hey there's some confidence level that this range captures that true median hourly wage so when they say there's a 95% confidence level they're saying that they're ninety four that there's a 95% probability that the true median is between these two numbers now if we're talking about a 90 percent confidence level if we're talking about a 90 percent confidence level that means we are less confident that the true median is between these two numbers in order to be less confident you would want to have even a narrower range you would want to range that is a subset of this range right over here let me make this clear so the range is twenty two dollars and seventy six cents all the way to fifty nine dollars and twenty four cents so they say it's a 95% confidence level that means I'm actually draw a number line here so let's say these are just points on the number line these are points on the number line so that's twenty two seventy six this is 59:24 they're 95% confident that the true median that the true median is going to be that is going to be between these two values so they're 95% confident the true median is there or the true median is there that the true median is there but there's still a 5% chance that may be the true median could be here it could be below this range or above this range now if we're talking about a lower confidence level 90 percent confidence level that means that the rain in this this this this range should be narrowed if you're gonna be less confident that means you want it hat or the only way you're gonna be less confident is if you have a narrower range if you grew if you had a broader range if it went from say here to here you'd be even more confident this type of a range you might have a ninety seven percent confidence level so ninety percent less confident you're looking at something that might look something like that might look something like that now let's look at the choices so this is $17 to sixty four ninety so this is actually more like this one you starting lower and you're ending higher so you should be even more if you're ninety-five percent confidence that this range capture you should be even more confident that this range captured it so this would actually maybe be a 97 or 98 who knows confidence level not a 90 percent confidence level so we can rule that out 20 48 to 53 32 so this one's interesting because it and it starts lower but then it ends lower two so I don't know what you could actually what what you could say it's based on the same yeah I don't know this this one's a little bit it depends kind of what the distribution that you selected was they didn't tell us a lot about that this is a little bit I know this one feels a little bit Shady 21:56 256 twelve well this is also similar it starts a little bit lower and then it ends a little bit lower so it's kind of a shifted the range and so it's this is also I wouldn't you know you don't know for sure that you're going to have I mean you're probably going to have a well they don't tell us a lot about the distribution so I'm not gonna make too many statements there now this last one goes from twenty five sixty five to fifty six thirty five so that's going to be something like that's going to be actually like from here to here this is going to be a narrower range so you would be less confident so this this could be something that represents a 90 percent a 90 percent confidence level so actually I would go with this one because this is kind of a purely this is a subset of the previous range so I like I like this choice all right over here