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Current time:0:00Total duration:5:19

Alma has developed a new kind of antibiotic for the antibiotic to be sufficiently effective it has to kill at least 90% of bacteria when applied to a harmful bacteria culture she applied her antibiotic to a petri dish full of harmful bacteria waited for it to take effect and then tried to estimate the percentage of dead bacteria in it she took a random sample of 300 bacteria and found that 94% of them were dead then she calculated the margin of error and found that the true percentage of dead bacteria is most likely to be above 90% so what's happening over here she's trying to figure out what percentage of the of the total population of bacteria died and maybe this is something about this bacteria maybe just when you look at it from you know with the naked eye you can't tell whether the bacteria died or not and so she decides to estimate the true percentage by sampling 300 individual bacterium or a sample add I always forget the singular case by sampling 300 bacteria and then in her sample she found that 94% of them were dead and then the margin of error tells us because the margin of error says that it's unlikely or that it's very likely that the true percentage is above 90% that means that given that you sample 300 bacteria it's very unlikely that the true percentage is below 90% so she could feel reasonably confident that in her petri dish more than 90 percent of the population did indeed die now let's answer these questions what type of statistical study did Alma use well she used a she's trying to estimate a parameter for a population in this case the parameter was the percentage of all of the bacteria that died she couldn't observe that directly so instead she took a random sample of the bacteria in the petri dish and she used she calculated statistic for them 94% of them were dead and that's her estimate for the population parameter the percentage of the population that died so this is when you're using a when you're using a random sample to generate a statistic which estimates a parameter for a population that's a sample study so she ran a sample study now the next question is is the study appropriate for the statistical questions it's supposed to answer so what was the question that she's trying to answer well at least the way it's written it seems like she's trying to answer whether or not her antibiotic works whether it's an effective antibiotic whether it's capable of killing bacteria and you might be tempted to say okay well look it looks like it killed it killed more than 90% of the bacteria it very likely killed more than 90 percent of the bacteria given given the the sample size and the margin error and all that but even if it is indeed the case that 95% of all of the bacteria died it doesn't necessarily mean that it was caused by the antibiotic maybe it was caused by the plastic in the petri dish maybe maybe the air in the petri dish was too cold or went bad or maybe it was handled in a weird way or maybe that bacteria was just a bad a bad a bad culture and it somehow it just spontaneously died on its own it's very she can't say with confidence that it was definitely it was definitely the antibiotic in order for her to make that statement she would have to run a proper experiment she would have to have a control and a treatment group where everything is equal except for the treatment group has the treatment so if she had two petri dishes that were helped that were that were kept in the same conditions with the same lighting the same air the same same material that the bacteria is growing on everything the same except for the treatment group has the antibiotic applied to it and then she saw that in the treatment group that most of the bacteria died while in the control group most of the bacteria didn't die then she could say okay it looks like the antibiotic caused the bacteria to dot to die that there was actual causality here so she would have had to run an experiment the more the most appropriate statistical study or the most appropriate study would have been a proper controlled experiment where you have a control group where they don't have the antibiotic and a treatment group where they do have the antibiotic so let's see one of the choices here where they say is the study appropriate so yes because she's in a purpose study no I don't like that answer oh because she can't know for certain that the true percentage of dead bacterias above 90% well I'm not going to click on that because even if she knew for certain that the true percentage of that dead bacteria were 95% she can't feel confident that it was due to the antibiotic once again it could be caused by the air conditioner could have been caused by the petri dish it could have been caused by the lighting in the room so no because the study didn't have a treatment at a control group yeah I would go with that one right over there yes because she found the antibiotic kills more than 90% of the harmful bacteria once again even if she no for knew for sure that more than 90% of the population had been killed she doesn't know that it was caused by the antibiotic it could have been caused by a whole bunch of things if she had a control group that had the exact same conditions and the antibiotic did and the bacteria didn't die then she could feel better that it was that the bacteria death was due to the antibiotic