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the relative frequency table below shows statistics from a study about the relationship between the amount of time a person spends using a computer before bed and the amount that a person sleeps each night for computer use each participant was classified as minimal moderate or extreme so let's look at the frequency table below so let's see that's the frequency table and let's see there's three categories of computer time just like they told us minimal moderate and extreme this is before they go to bed or at night and then they have the three categories of how much they're sleeping five or few hours per night five to seven hours per night or seven or more hours okay so that's fair enough so let's see what they want us to do so they tell us suppose there were 17 people in the study who were both in moderate computer users and got five to seven hours of sleep so moderate five to seven so this category right over here there were 17 people in this category over here and just to mark that let me I copy and pasted this chart onto my scratch pad so so I can write on it so this group they're telling us this group and my pen is really acting up I don't understand what's going on this group right over here there are 17 people so that group right over there is 17 people now what are they asking us they're saying so they're saying how many people in the study were both extreme computer users and got 5 to 7 hours of sleep round to the nearest whole number so extreme and got 5 to 7 get my scratch pad out so they're saying how many people are in how many people are in this in this bucket in this bucket right over here I on they have to replace my pen tablet or something that why it's getting all splotchy like this so how would we think about this there's 17 people in this group how many people are in this group well they tell us that 17 is 34 percent of the row of the row total so I guess you could say 17 is 34 point three percent of the moderate of the moderate computer users or you could say that 17 is thirty percent of the people who slept five to seven hours each night or you could say 17 is 10% is 10% of the total of the total number of people so let's just go with that we could figure out the total number of people so 10% just let me write it this way so 10% 10% of the total 10% of total is going to be equal to 17 or that the total just divide both sides by 10% is equal to 17 divided by 10% which is the same thing as 17 over 0.1 which of course is equal to 170 so the total is 170 and they tell us that extreme extreme computer users represent extreme computer users who sleep 5 to 7 hours per night represent 11.7% 11.7% of the total so they answer their question of how many people were extreme computer users who sleep 5 to 7 hours per night that's eleven point seven percent of 170 so let's go back over here so we actually have a little calculator tool here so it's it's eleven point seven percent which is zero point one one seven times 170 times 170 is and let me make sure that you can see what I'm doing by scrolling over a little bit x 170 is equal to nineteen point eight nine so if we're rounding to the nearest whole that's going to be 20 people 20 people and then they are going to ask us some questions they say does the table show evidence of an association between being a minimal computer user and getting seven hours of sleep or more so let's just look at the chart so an association between being a minimal computer user and getting seven hours of sleep or more so it looks like minimal computer users so that's this these are the minimal computer users who get seven or more hours of sleep and there's a couple of ways to read this so you could say that fifty-one percent of men all computer users get seven or more hours of sleep you could say that of the people who get seven or more hours of sleep 55 percent are minimal computer users and of course this one just says that minimal computer users who get seven or more hours of sleep represent 18.3 percent of all of the people who were surveyed so let's look at the choices and when I just actually before I even look at the choices let's see if there's an association it does look like if you look at if you look at minimal computer users it looks like a small percentage only 16% get five or few hours a higher percentage gets five to seven hours and 51 percent the highest percentage gets seven or more so it looks like for minimal computer you for minimal computer users it looks like the the distribution is definitely weighted towards getting more getting more sleep and actually for example if we look at the extreme computer users it's the opposite trend forty per six forty seven percent have five or few hours per night 33 percent five to seven hours and then only 19 percent get seven or more and it looks like the moderate is someplace in between so just looking at this just looking at at each of these rows it looks like there's a trend where you use less if you use a computer for less time you're more likely to have more sleep and likewise if you use a computer more you're more likely to have less sleep another way to think about it when you look at the people who are getting seven or more hours of sleep a majority of them a majority of them are minimal computer users and there's three categories so for 55% to be minimal computer users really does feel like the minimal computer users are are more you know they're definitely more disproportionately representing the people who are getting seven or disproportionately represented in this category of seven or more hours of sleep and you see that the extreme computer users in this category they represent only 20% of this category so it does look like there is an association between minimal computer use and getting seven or more hours of sleep but let's look at the actual choices they give us does the table show evidence of an association between a minimal computer user and getting seven hours of sleep or more so yes because 35.1% are extreme computer users and twenty-nine point one percent of people are modern well I go with the yes but this doesn't seem to really back up the claim this is just giving us some random data about the percentage that are extreme computer users or moderate computer users no well I already explained why I go with yes that there's does seem to be a trend and I don't even believe what the statement is because the total column percentages are essentially equal we see that the total column that the column percentage is the column percentages are not equal for the various for for people who are getting seven hours or more of sleep so we see that right over here 55 25 2000 with that one either yes because 51% 51% of minimal computers get seven or more hours of sleep and only 33% of all computer users get seven or more hours yeah I mean that that seems pretty good fifty-one percent a minimal computer users get seven or more hours of sleep and only 33% of all computer users get seventy get seven or more hours of sleep so that looks like a pretty good explanation so I'll check that but let's just review all of them no well I already said I think it's yes but because the total percentage of extreme users who get five to seven hours of sleep is the same as a total percentage of moderate computer users who get five to seven hours of sleep so that doesn't it doesn't really be it's not touching on the point that we're looking for yes because 55% of people who get 75 who get seven or more hours of minimal computer users and only 35% of all people are minimal computer users actually I'll go with this as well oh yeah this is this is a multi-select here so I could select that one as well so this one we're looking at of the so here we looked we looked at the percentage of minimal computer users who get seven hours of sleep and we saw that percentage is higher than for the whole population here we're looking of we're looking at the people who get seven or more hours of sleep and we're saying well 55 percent of them 55 percent of them are minimal computer 50 55 percent of them are minimal computer users even though only 35 percent of all the people are minimal computer users so I would go with both of these and so let us check our answer and we it right