In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Eighteen randomly selected plots of land were treated with fertilizer A. The average yield, in pounds, was 457 with a standard deviation of 38. Twelve randomly selected plots were treated with fertilizer B. The average yield was 394 pounds with a standard deviation of 23. Find a 99% confidence interval for the difference between the mean yields for the two fertilizers. (Round down the degrees of freedom to the nearest integer and round the final answers to two decimal places.)

(31.25 ; 94.75)

Step-by-step explanation:

Given :

Sample size, n1 = 18

Mean, x1 = 457

Standard deviation, s1 = 38

Sample size, n2 = 12

Mean, x2 = 394

Standard deviation, s2 = 23

Confidence interval :

x1 - x2 ± Tcritical * Standard Error

x1 - x2 = 457 - 394 = 63

Standard Error = sqrt[(s1²/n1 + s2²/n2)]

Standard Error = sqrt((38^2/18)+ (23^2/12)) =11.149

Tcritical = Tα/2, df

df = n1 + n2 - 2 = 18 + 12 - 2 = 28

Using the Tcritical value calculator :

Tcritical at 0.01, 28 = 2.763

Confidence interval :

x1 - x2 ± Tcritical * Standard Error

63 ± (2.763*11.149)

63 ± 31.74687

Lower boundary = 63 - 31.74687 = 31.253

Upper boundary = 63 + 31.74687 = 94.747

(31.25; 94.75)

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

c.

step-by-step explanation: