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15. The numbers (in thousands) of farms per state found in three sections of the country are listed below: Test the claim at & = 0.05 that the mean number of fa...

Question

15. The numbers (in thousands) of farms per state found in three sections of the country are listed below: Test the claim at & = 0.05 that the mean number of farms is the same across these three geographic divisions_ Eastern third Middle third Western third48 34 10 3895 52 64 6429 40 40 68Source: NY Times Almanac:

15. The numbers (in thousands) of farms per state found in three sections of the country are listed below: Test the claim at & = 0.05 that the mean number of farms is the same across these three geographic divisions_ Eastern third Middle third Western third 48 34 10 38 95 52 64 64 29 40 40 68 Source: NY Times Almanac:



Answers

Number of Farms A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with $90 \%$ confidence. Assume $\sigma=31.0 .$ $$ \begin{array}{cccccccccc}{47} & {95} & {54} & {33} & {64} & {4} & {8} & {57} & {9} & {80} \\ {8} & {90} & {3} & {49} & {4} & {44} & {79} & {80} & {48} & {16} \\ {68} & {7} & {15} & {21} & {52} & {6} & {78} & {109} & {40} & {50} \\ {29} & {} & {} & {} & {} & {}\end{array} $$

Begin by setting up your graph on our X axis, we're gonna put our years now. I am putting a line break here. Since we're starting in 1950 and then going up to 2007 on our Y axis. Let's put our number of farms in millions. You do have to specify that in your label. Once you have this down, begin filling in your bars. In 1950 there was 5.6 million. So it's make a line at 5.6. And the maker bar. Now, this specified a bar graph, not a history, Graham. So our bars should not be touching. In 1960 there was four million to make a lineup for and then come down in 1970. There was 2.9 million. So 2.9 is gonna be just under three. So somewhere around here in 1980 there was 2.4, so we're gonna be just under halfway up in 1990 there was 2.1, so we're gonna be just barely above two. In 2000 there was a slight uptick to 2.2. Now make sure it's slight, but it's visible on your graph. Then in 2007 there's once again 2.1, So that should be in line with your 1990 bar. So now you have your paragraph. Just remember, you need gaps between them because this is not a hist a gram.

Begin by setting up your church on our X axis, we're gonna have our years now. Be sure to label it as years. I'm using a line break here since we're starting at 1950 and go in 2007 when are Y Axis? We're gonna have to label it as the average size of farms in acres. You need to be very clear that all that information is in there. It's not just the size of farms, it's the ever size and we need to include the units. Now, I'm including a line break here because I noticed that my lowest number was 213. So you started 200 and my highest was 460. So I'm gonna put my highest number here. Coming in. My fifties is 500. Since we're doing a line graph, we're gonna start making dots for each year. For the average number of acres in 1950 the average was 213 so that's about here. In 1960 it was 297. So that's gonna be just barely under 300 in 1970 is 304 74. So that's a paroxysm innately here. About midway between 3 50 and 400 in 1980 we still been increased toe 4 25 So again, kind of in between 404. 50. In 1990 it was 204 160. So, again, just barely above the 450 line that in 2000 we had a decrease to 436. So that is going to be approximately right here and then 2007. It was 449. So it's gonna be just under 4 50 So kind of here. Now we need to collect connector lines now. Make straight lines between each of your doubts. You're not making a line of best fit and said it's like connect the dots. So there you have your line graph for the average size of farms in acres through the years

In problem that he ate. We have some deter on the old production yield by Eka for 39 countries from the 68 upper Midwest area of the United States, and we're going to use this data to tell whether there's a significant difference in the many illiterates. For the sixth. It's so these are the six categories here, the six sticks and we're going to be using Alfa. It could 0.5 okay, so to tell whether there's a significant difference in the means yield rates for the sixth, it's would have to perform analysis of variance. So we go to data, deter analyses, a nova single factor, then press OK, then for the it would change. We want to select the data for the sixth. It's you need to ignore the last the fast column because it's just available. Then they would want to ensuring that the details group by columns, and that the Liberals and Fast Room and the half A 0.6 and the outputs should be right next to the details that sell any press with King. And these are the results with the analysis of variance at the 0.0 point 05 Significant comes now we check the Peabody and the Peabody for this deter is 0.9 5879 and the offer is 0.5 So because the P value is greater than the level of significance Alice what? He failed to reject the night services. So this indicates that oh, from the sample, there's no the evidence is not enough evidence to show that there is a significant difference in the mean yield rates For the sixth. It's next part b of the question the good to drug ra that demonstrates the results founding. But and the best graph here would be a box plot. So we need to select the six columns and then we go to incite and you pick these box and whisker. Dad grabbed. Okay, so the box and whisker diagram here with box blood side by side box plot is showing us the the results, and we're going to explain the meaning off the results using the graft. So, as you can see, the grass are somewhat showing very slight differences between the six, uh, six regions. So, as you can see here they is a lot of overlapping to even the first US, the first region on a The rest of the regions are not so different from each other at 0.5 level of significance.

This table was brought to you by the U. S. Department of Agriculture. Uh and then the book took out a few values over here to put them back in. So we'll start with this full owner. We got our total of 1429 and we just got to add up all these other numbers here. This turns out to not be 16 or what is there Problem. is what it turns out to be. And then we have the total for this role right here Is going to turn out to be 744 And then we can calculate the total for everything here. And that is going to be 2130. That's gonna be the summer all the way over here. And then we can fill in the blank for this tenant. That's gonna be 150 And then finally we can fill out this blank for 10ant right there It's gonna be 33 And then part time owner, last one left is going to be 153 Now were asked a series of questions. Um the first one is, how many cells does this contingency table have while this is going to be 12345 times three. So five times three is equal to 15 cells. Yeah. And then we have, how many farms have under 50 acres so acres is under 50 over here. That's gonna be for a 744 Maybe we'll use a different color. And then how many farms are tenant operated? So tenant is in this column, that means 150 of them are tenants operated. We'll get rid of that circle. And then how many farms are operated by part time owners and have between 599 acres. So between 599 is this role right here? Okay. And part time is going to be here apart honor. That's going to be 91. And then how many farms are operated? Oh, I lost my track. How many farms are not full owner operated? So that is going to be Right here. 1429. How many are not? That's just gonna be the sum of 551 Plus 150. This is equal to 700 one. I don't know why that calculation was hard for me. And then the last question, we have, How many Tenants operated farms have 180 acres or more. So we got over here, we're looking at everything below there and we are looking at Tennant operated farms. So it's gonna be this one right here, so we're gonna have for e 33 plus 17 plus 18, This is gonna be 33 plus 35, so 68.


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