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Which the following aual itative Va5 able? Meight kilograms Number days Ethnicity without precip tation Ave rage daily Cemperatureexperiment only one answer)the ind...

Question

Which the following aual itative Va5 able? Meight kilograms Number days Ethnicity without precip tation Ave rage daily Cemperatureexperiment only one answer)the independent variable memory,(choothe effect of sleepNumber Cf hourg sleep Recall acore mnemory test Gender Ehe supjects Gender Ene experimenterFor Lne acores Lollowing Lofmula:10, P/10017 ,25, calculate the 25th percentile uging ehe2.25

Which the following aual itative Va5 able? Meight kilograms Number days Ethnicity without precip tation Ave rage daily Cemperature experiment only one answer) the independent variable memory, (choo the effect of sleep Number Cf hourg sleep Recall acore mnemory test Gender Ehe supjects Gender Ene experimenter For Lne acores Lollowing Lofmula: 10, P/100 17 , 25, calculate the 25th percentile uging ehe 2.25



Answers

Which of the following scenarios should be analyzed as paired data?
a) Spouses are asked about the number of hours of sleep they get each night. We want to see if husbands get more sleep than wives.
b) 50 insomnia patients are given a placebo and 50 are given a mild sedative. Which subjects sleep more hours?
c) A group of college freshmen and a group of sophomores are asked about the quality of the university cafeteria. Do students’ opinions change during their time at school?

Within my study of insufficient sleep. I am taking a group of 10 respondents any time I'm looking at a small group within a larger group like this. 10 respondents I'm looking at to find the probability of a certain outcome among those small that small subgroup of people really use. The following formula. The probability of our successes in N trials in this case, the number of trials is 10. That's my subgroup. About 10 respondents I'm looking at. Our success is, well, this is five people not getting enough sleep. So for this particular case, that will be five successes in 10 trials, and that's going to equal the combination of end things Taken R at a time Times P to the R repeat is the probability of success at times. Q to the n minus. R and cue is the probability of failure. However, we define success and failure for our particular scenario. Okay, so in this case, the probability that exactly five got enough sleep out of 10 respondents. Well, that's the probability of 10 things taken five at a time. Now for these five, I'll be raising it to the fifth Power are is five here. What is a success? Well, they got enough sleep every night. Well, that means they had no days where they had insufficient sleep. So on my chart, the probability of having zero is 0.23 now and minus R is also gonna be five. And I want to find cue the probability of failure. Well, that's gonna be the complement of getting enough sleep 50.23 So that's going to be 0.77 Because everybody else will fall into that category. If I plug that into my calculator, I find that the probability of exactly five people getting enough sleep every night is 0.439

I am taking a small group of 10 respondents out of everybody who responded to this survey. And out of those 10 respondents, what's the probability that exactly four did not get enough sleep for somewhere between 1 to 13 days? Any time we're finding that type of probability, the probability of a certain number of people within a group, we're going to use the following formula, the probability of our successes in n trials. So in this case, that's 10 trials of out 10 respondents. Four Not getting enough sleep. My our would be 44 successes in 10 trials. This is what our formula looks like. The combination of end things taken R at a time times p to the R, where P is the probability of a success. Times Q to the n minus. R and Q is the probability of a failure. However, we define success and failure within the particular problem we're looking at. So in this case, the probability off four in my group of 10 well, that's going to be the combination of 10 things taken for a time. Well, what I'm looking at us for not getting enough sleep for days for 1 to 13 days. So according to my chart, that probability is 130.45 And there's four of those. So that the race to the fourth power, the probability of it not happening, would be the complement of 0.45 or 0.55 And I'm going to raise that to the n minus R power or the sixth Power. If I put that into my calculator, I find that the probability is point to 38

Right. The average time spent sleeping in ours for a group of medical residents as a hospital can be approximated by a normal distribution. So we're going to draw our normal curve And you had to look at the figure to find that the average or the mean was 6.1 and the standard deviation Was 1.0. So for part a we're trying to find the shortest time spent sleeping that would still place the resident in the top five of sleeping times, so the top five would be right here. So now, if there's 5 to the right of that boundary line, that means there's 95 to the left. So ultimately we're trying to find the sleep time in hours. But in order to get there, we are going to have to find the Z score first. And the Z score that is associated with. That can be found by using your inverse norm function on your graphing calculator. And when you use inverse norm, you have to provide the area in the left tail, followed by the mean, followed by the standard deviation. So in our left tail we've got .95, Not a .05. Since we are finding a Z score, the mean of a Z score, or the standard normal curve is zero and the standard deviation is one. So I'm gonna bring in my graphing calculator and I'm gonna do second. There's to access my distributions functions and it's number three in my menu. So the area in the left tail followed by the mean of the standard normal curve. And the standard deviation of the standard normal curve gets me a Z score of approximately 1.645 So that means on the Z scale now remember the mean is zero, So we just found a Z score. So right here would have a Z score of 1.645 So our goal is to find that X value. So we need to transition back. And the way we'll transition back is we'll use the formula you have for Z scores. And you know, to find a Z score, you take x minus mu divided by sigma. So if I were to use some algebra skills and calculated my cross products, I would end up with X minus mu is equivalent to Z times sigma. If I then added mu to both sides and isolate the X. I've got a new formula that says X is equal to mu plus Z times sigma. So I'm going to apply that formula to find the boundary line That separates the top five of sleep types. So our average was 6.1, We found the Z score to be 1645 And our standard deviation was 1.0. So that ends up where 7 745 hours Would be the shortest time spent sleeping. That still places a resident in the top five of sleep times. So that was part A. Now let's go on to part B. So in part B we're going to draw the same curve, We're still going to have a mean of 6.1, but this time it wants to know About the Middle 50%. So we're going to draw a line here and a line here And say that this is 50 of the curve. So now the whole entire curve would be 100%. So if 50 is in the center, that means there's 50 left over to be split evenly between those two tails, which would make the left tail to be .25 And the right details to be .25. Again, we're going to have to find the Z scores affiliated with each of those boundaries. So to find this Z score, we're going to do in verse norm. Again, it's the value in the left tail, so left of this line Would be .25. The mean of the standard normal is zero and the standard deviation is one. So we bring in my calculator, second vares Inverse norm of 2501. And I'm going to get a Z score of approximately negative .67. So this is the score right here is negative 0.67 So now I want to find the Z score on the other, the right hand boundary. So I'm gonna use Z equals inverse norm. But this time from this line into the left tail would be 75 of the curve. And again our standard deviation and our average didn't change. So I'm going to bring in the calculator, inverse norm 0.75 With a mean of zero and a standard deviation of one gets me of Z score of positive 67 Yeah. So now we want to find each corresponding X value. So the first one and do this one, we're gonna say X equals mu plus Z time sigma. So arm you was 6.1. The Z score associated with that boundary line was negative 0.67 And the standard deviation 1.0 Gets me seven No, sir, it gets me five 43 hours. And then doing the other ones were going to do this one right here, X equals mu plus Z times sigma. So we're going to get 6.1 plus the Z score on this boundary line was positive .667. And we will get 6.77 hours. So just to recap part a what is the shortest time spent sleeping? That would place a resident in the top 5%. That's going to be 774, 5 hours and part B. Between what two values does the Middle 50 of the sleep times lie, The middle 50% is going to lie between 543 hours And 677 hours.

In this case, it is said that her conclusions were based on a sample data that consisted of 4500 mail responses from 100,000 questionnaires that present to women. So the data waas the responses that she received. So this is an example of a convenience sample. The convenience simple. What? This is a convenience sample.


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