Answer to Question #322320 in General Chemistry for carlington

Question

Question 1

Table 2 gives the recovery of bromide from spiked samples of vegetable matter, measured by Gas-liquid chromatographic method. The same amount of bromide was added to each specimen.

Table 2: Recovery of bromide from spiked samples of vegetable matter

Tomato 777 790 759 790 770 758 764

Cucumber 782 773 778 765 789 797 782

a) Test whether the recoveries from the two vegetables have variances which differ significantly. [10 Marks]

b) Test whether the mean recovery rates differ significantly.

Answer 1

 It's number 22, and this is almost identical to number 21. Just a different data set because it's a different type of soil. And we're asked to find the mean concentration of dissolved organic carbon, carbon, but not an organic soil, but just mineral soil. So the data set, it's a little bit longer, they're actually 47 data values. And you can certainly find the mean and the standard deviation of on your own if you want, but they actually give you that information, so they do a lot of the work for you, which is nice, and I did check it and it is accurate, But X bar the mean is 10.03. That was given standard deviation was 4.98. And then the the data values, that's the only thing they didn't give you, but in his 47. So if you count up all those data values, there are 47 of them. And we're asked to find uh the 99% confidence interval. And then we're going to interpret that. So I'm still going to use technology, so I'm gonna use the T. I. T. For. But you can use whatever technology you want. Or you can certainly use the formula. And if you go to stat and then tests, we're gonna use the tea interval, right? We use the tea interval because we don't know that population standard deviation. If we knew the population standard deviation, we would use the Z. Interval. But we don't so we have to use the tea interval so I'm gonna go to eight and make sure that the summary stats here is highlighted. And if you go down and just fill in your information here, so x bar is 10.03. Standard deviation is 4.98, The sample size is 47, and then the sea levels .99 for that 99%. And then whenever we calculate this top band that gives us our confidence interval. So let's go and write that down. It's eight 8.0781 And 11.982. Now, if you actually use the data you're gonna get in fact slightly more accurate answer, but it's pretty close to the same. So uh this is just if you're given the summary stats, Okay, now it's time to actually interpret that. So there are actually two parts, we're going to compare it to number 21 as well. But the interpretation here and these interpretations kind of follow the same pattern. But we're going to say We are 99% confident that the mean concentration of dissolved organic carbon collected from mineral soil is between eight point 0781 And 11 9, 8 2 milligrams per liter. And then part B were asked to I guess I should technically put a period at the end of it tonight. Okay, so part B uh compared to the previous problem where we look at organic material and um just as a reference, I'll go and write it up here. But that Previous problem, it was 12 402 and 19 438 Okay, so this is number 21 And we compare it and basically to compare it, you see if there's a difference, a significant difference between the two and there is because there is no overlap here. So I had this number of this 11.92, had it been like 13, there would be a slight overlap. So there's not a significant difference. But since there is no overlap, there is a significant difference between the two. So that's basically we're gonna say so yes, they are different, I'll say significantly different because there is no overlap between The two confidence intervals. Okay, so that's basically we look forward to see if the if two data sets are in fact or have the same mean or um or a significantly different meanings. You look at those confidence intervals and if they are um if there is no overlap between the two, then that means there is a statistically significant difference between the two.