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(3 pts:) Calculate the population mean . population standard deviation, and population size of the ant colony Place the answers in the space indicated in "Shee...

Question

(3 pts:) Calculate the population mean . population standard deviation, and population size of the ant colony Place the answers in the space indicated in "Sheet (3 pts:) Calculate the sample mean, sample standard deviation, and sample size of the first 25 ants in the data set (cells A2 to A26). Place the answers in the indicated cells in " Sheeth".3) (2 pts ) Compare the values of the sample parameters to the population parameters. Does the data indicate bias in the sampling? Expl

(3 pts:) Calculate the population mean . population standard deviation, and population size of the ant colony Place the answers in the space indicated in "Sheet (3 pts:) Calculate the sample mean, sample standard deviation, and sample size of the first 25 ants in the data set (cells A2 to A26). Place the answers in the indicated cells in " Sheeth". 3) (2 pts ) Compare the values of the sample parameters to the population parameters. Does the data indicate bias in the sampling? Explain,



Answers

Find the mean and standard deviation of the population. List all samples (with replacement of the given size from that population and find the mean of each. Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population. The scores of three students in a study group on a test are $98,95,$ and 93 Use a sample size of 3

Soon this problem, we're going to be using the data set 2345 and six and report A. We want to find the range. And to do that, you just take the highest value minus the lowest value, which gives you the range Thanks. Which in this case, is for heartbeat. We want to use the defining formula to compute the sample standard deviation. So that's just equal to the square root of the sum X minus X bar, which is the main squared and X is just your individual data point over in minus one, where little in is the number of data points you have. So in this case, it would be from Well, first, we have to find the mean, so expert in this case, which would be the song of all of your data points over the number of data points in your set. So let's just complete that really quick. Mhm. So it's going to be four mhm. So up here, we would have, um, two minus four squared. So four, and then I'm just gonna do that. Um, the data point minus in the unit for all of the data points and taking the square that over and minus ones, they'd be five minus one mhm. And this will give us a standard deviation of 1.58 and then in part C, we're going to use the defining formula to compute the population standard deviation sigma. So, Neil, for export as we found above, is just going to be for and then Sigma is equal to the square root. The sum of X minus X bar squared over and we're in is just the number of data points that we have. So again, for our data set, that would look like four post one post cereal post one plus four all over five. Because that's our entire dataset. Whereas for the standard deviation at end minus one, this will give us a signal value of 1.41

Okay, So when you roll a die, the probability of getting nod number is just three out of six. Probably getting a tour for two out of six. The probability of getting six so we can create a summarised table for the probabilities and payoffs in the roll of a die where X denotes the winning amount. So my name about So when X is you go to X you p elex just a probability is 36 26 on six x times X zero by six Just a X squared x You cannot be 0 to 6. 100. Okay, so now we can try to calculate expected value if you're prospected. Earnings Dfx. Biologist Vehicle to signal. Thanks. Thanks. So you times 36 this six six give you to now we got variants just far X. That's actually good to signal X squared times. Thanks. Minus signal x 17 to scream 70 miles. Four. Finally last with this question, find the standard deviation. Thanks. So just S T X. That's actually going to the variance Screw with very thanks. Just standard deviation Scrape Give us Chine for $3.6

All right, so we have X being 1234 and five. Then we have Xmas export here and X minus export squared. Mhm. And so for a the range is going to be range equals largest number My smallest number Just four. Then we need to find the standard deviation, for example. So we need thio, Then calculate the mean, which is gonna be three. So we have one minus three to minus three three minus 34 minus three and five minus three equals negative to negative. 101 and two. Then we're going Thio square those values to give us 41014 And then we can use our formula for us which is square root of the some of X minus export squared over and minus one. Alright, so continuing on, we know that some of X equals 15 in the sun of X minus, exports squared equals 10. Now, with this in mind, we confined, uh, 10 over four, which is going to be screw root of 2.5. And now we can also find Sigma, which is pretty much the exact same thing except the denominators different. There's going to be 10/5 because it's going not be subtracted by one, and that's going to give us a square root of two. And here is our final set of answers.

So this problem were given the data set at 1234 and five reporting. We want to find the range. So the range for data set is just the highest value, minus the lowest value in this case is for and then for part D. We want to use the defining formula to compute the sample standard deviation, um, and the standard deviation. The formula for that is just the square root of the sum of X minus X bar squared over n minus one, where X is just each individual data point. X bar is the mean and is the number of values in our data set. So to compute this, we need to compute the mean So it's just going to be the sum of each individual data points over end. So in this case would be one plus two plus three plus four plus 5/5. And so that's going to be three. And now we can go ahead and solve for R um, standard deviation. So just plugging in for the first term and the sun would be one minus three squared, plus two minus three squared and so on minus over five minus one. So if we put all of that and we'll get a standard deviation of 1.58 and then for part C, we want to compute the population standard deviation Sigma using the defining formula. And so sigma here it's going to just be the square root of the son of X minus X bar squared over n where big end is just the number of data points that we have. And now we can just plug in our values and solve um, just like we did with B. Except this time it will be over five and not for and I don't want to be four point, it'll end up being 1.41


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