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University financial aid office Mants to know how much it can expect students cam from summcr employment This information 'wll be used to set the level of fina...

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University financial aid office Mants to know how much it can expect students cam from summcr employment This information 'wll be used to set the level of financial aid The population contains 975 students who have completed at Icast one year of study but have not et graduated . questionnain will be sent to rndom sample of 50 of thesc students, drawn from an alphabetized list.Explain clearly how you would use random digits table t0 choose simple random sample of 50 students from this popul

university financial aid office Mants to know how much it can expect students cam from summcr employment This information 'wll be used to set the level of financial aid The population contains 975 students who have completed at Icast one year of study but have not et graduated . questionnain will be sent to rndom sample of 50 of thesc students, drawn from an alphabetized list. Explain clearly how you would use random digits table t0 choose simple random sample of 50 students from this population #fcJUp , 07od| {LD fJ"J e 60mjeM elr: O8lv ol3A ! etaal boji 5m,n IeLicz &te /1 nuzaup bunze 3T ^Jierl | FA ? WFr J37c/ 6 Df2JnI aiqeld 1q"e Jo lahriu {InTYJ Vf' n" (Ic ~ilt & Wh5ly2.216"| '1-u 3t0 77't| (6) Bcginning line 120 in thc random digits table below; show thc first 10 students that are sclected using te method described part (b) . Mark on the table= wnitc below the table t0 show your method clearly. 120 35476 55970 39421 65850 04266 58435 43742 11937 09984 29077 14863 61683 47052 62224 51025 121 71487 13873 81598 95052 90908 73592 75186 87136 95761 122 (c) Tne surve; Lome be conducted again thc following acadcmic ycar only this tmc thcy want rndom sample. Suggcst Uariallc stratily by. Justify your cholce stratificd



Answers

A small community college employs 87 full-time faculty members. To gain the faculty's opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 87. (a) Using Table I from Appendix $A$, the president closes his eyes and drops his ink pen on the table. It points to the digit in row $5,$ column $22 .$ Using this position as the starting point and proceeding downward, determine the numbers for the 9 faculty members who will be included in the sample. (b) If the president uses the randInt( feature of a graphing calculator with a seed value of $47,$ determine the numbers for the 9 faculty members who will be included in the sample.

There is absolutely nothing to do with this question. Again, you just have to look at appendix a. You just have to look at what value you have in row 11 and call him 32 post that. You just have to no doubt the numbers. So there is absolutely nothing to do with this. And in the second one, what we have to do is very important thing over here is to set the seed The seed to 142. Now, what actually is a seed? Uh what A C. Does this? It helps you regenerate the same numbers, right? For example, if you have a random generator, if you have a package, a computer package that gives you a random numbers. Now, what do you do to make sure that you get the same sample of random numbers the next time you set a proceed? So this is what you have to do in party. Again, the values are going to differ from student to student who do this exercise. Right? So this is subjective question. There is no right or wrong answer.

This is a problem. # 29 We are given a set of data regarding regarding the per capita disposable income for each of the 50 States and District Columbia. First we will construct a frequency distribution Given that the lower bound of our class is 20,000 and our class with our 2500. We will get the following for our income. Mhm. I'll just round both of these classes to make it easier to fit. So we have 20- 25 K. 22.5. Mhm. 22 5-25, 25-27 5 27.5-30 30 to 32.5 32 5-35, 35 to 37.5 37 5 to 40 and finally 40- 42.5. Now these are not inclusive of the bounds. This is obviously this will be like 22499, I just ordered like this to make it easier to ride out for our frequencies. If we count each of these data points, we get the following three, 10, 14, 12, seven, two, two, zero and one. And when we calculate our relative frequency we get 5.9%,, 19.6%,, 27.5%,, 23.5%,, 13.7%,, 3.9%,, 3.9%,, 0% And 2.0%. So as we can see most of our data is in the top part of our data set. And when you construct your hissed a gram, it does seem to follow this so it is very slightly right skewed. If we are then to change our class sizes to be 4000 wide you will find that the data is significantly more skewed left as our relative frequencies will drop to 19.6%,, 43 0.1% 27.5%,, 5.9 And 2% for the last two classes that we would have. So as you can see, this data is significantly more right. Skewed. This set of data with these smaller classes is a much more precise way of representing this data.

Problem number. Ah nine. Question A. The numbers for the nine faculty members included in the sample are 83 67 84 38 22 24 36 58 and 34. We start in Row five, Column 21 move downward. Since our data have two digits, we select two digit numbers from the table using column 21 22. So we select numbers between one and 87 rejecting zero and zero. There is greater than 87 those already repeated, which can be that zone number for the nine faculty members using the technology are 79 12, 18, 56 nine, 25 48 84 and 17. Any statistical software will be used to generate nine random numbers between one and 87 here. Um, Microsoft Excel was used for the purpose, so we generate this around them. Nine. Run them saying

In this question. To start off, we're given this relationship between lambda and P. Then in part A We are told that why is a binomial random variable based on parameters N. And lambda. Therefore why divided by N. Is an unbiased estimator for lambda. And we are asked to derive an unbiased estimator for P based on why we can rearrange the equation at the top of the sheet to give the following. This means that an estimator for P is given by the following. So that is our estimator for P. And now given and equals 80 And why equals 20. We want to find our estimate for P. So we just plug this into the formula for estimator And this comes out to 0.2. For part B. We want to show that our estimator is unbiased. So we really want to show that the expected value of our estimator is equal to P. So this is equal to the expected value of two. Y over em -0.3. That's just using this equation with why over and is equal to lambda. And then using the linearity of expectation. This can be re expressed as the following. So this is two times lambda And the expectation of .3 is .3. And this is equal to P. Since the expected value of our estimator is the parameter we're estimating for it is an unbiased estimator. And then for part C we are given a slightly different set up for the question which would result in this relationship between lambda and P Would now be 0.7 times P Plus 0.3 times 0.3. And now we are asked what our estimator for P would be the estimator for lambda remains Why over em since why is still a binomial random variable, the estimator for P is equal to the estimated Verlander -0.09, Divided by 0.7. And that's done simply by solving for P in this equation and then simply re expressing this, substituting why over. In for for the estimated for lambda, we get why over in -0.09 Over a 0.7. So this is now our estimator for P.


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