T-tests are used to compare up to 2 groups (can also be used for one). If you had more than 2 groups, you will have to do multiple 2-group comparisons/tests, for all the possible pairs, and since a type 1 error is associated with each comparison, multiple comparisons will result in greater risk...
Your null hypothesis always suggests equality and that any differences detected are simply due to chance. So a rejection of the null will be suggesting just the opposite, that observed differences are most likely not due to chance.
Looking at the rest of your answer choices, in addition to normality, your samples are indeed also assumed to be random and of equal variances before an F-test can be performed.
The deviation of variation of group means from one another is your variation between the groups.
Your null hypothesis is always your hypothesis of equality. Of the five choices, the only one suggesting equality is:
The F-ratio is a ratio of the variation between your treatments to the variation
within your treatments.
Or, put algebraically, F = (variation between treatments) / (variation
The within-treatment variation is the variation due to chance. So, obviously,...
add the numbers together: 9+3+11 = 23
you want the ratio of total number of grapes to total number of fruits
this should be consistent no matter how many fruits you have, so:
9/23 = x/161
cross-multiply and solve for x (number of grapes in a total of 161 fruits)
okay, that's an upside-down U and the maximum value is at the top
if you put the function in vertex form you can easily find the vertex:
group the first two terms and factor out the negative (essentially factoring out -1):
p = - (x²-14x) + 54
complete the square by taking...
bring all terms to one side and set equal to 0
factor out 2
2(2n²+6n+3)=0 ===> 2n²+6n+3=0
complete the square
2(n²+3n+9/4) + 3 = 0 + 9/2 ===> 2(n+3/2)² = 3/2 ===> (n+3/2)² = 3/4
take square root of...
--------- = 10/2 = 5/1 = 5
separate the first two terms on the left and factor out 5
5(m² + (12/5)m ) + 6 = 0
take half the middle coefficient (12/5), square it, and add it to the terms in parentheses
5(m² + (12/5)m + 36/25) + 6 = 0 + 36/5 (this has the effect of adding 36/5 to both sides)
assuming those are 3 terms and not 2 you should start by noting all restrictions for x. In this case, x cannot be 0 because we can't divide by 0.
multiply both sides by the lcm (2x)
9 + 2x = 8 ===>
2x = -1 ===>
x = -1/2
you need to simplify the expression by collecting like terms:
(-9 + 4)x² + (6 + -1)x + (2 + -1) = -5x² + 5x + 1
range value is the y value
domain value is the x value
(a) find y when x = 0
y = 2x-1 = 2(0)-1 = -1
y = -1
(b) find x when y = 5
5 = 2x-1
6 = 2x
x = 3
if the roots are r1 and r2, then the simplest equation is the quadratic:
(x-r1)(x-r2) = 0
since yours are -3 and 5, the simplest (quadratic) equation is:
(x - -3)(x - 5) = 0
(x+3)(x-5) = 0
which expands to x²-2x-15 = 0
simple interest equations:
A = P(1+rt) = P + Prt
I = Prt
A = accumulated...
Cost = $31/$1000 * $24000 = $744
Quarterly payment = $744 / 4 = $186
4x - y = 7
-2x + y = -5 (rearranging the first equation)
2x = 2 ...
check the number of digits in the number
you have 3 possibilities:
the only 3-digit candidate you have is 100 and that results in a 1, so this is an easy case
for a 1-digit number the only way for the digits to add to 1 is for that number to be =...
suiye is right, and that way is probably even quicker, but another way to arrive at the answer is to set up an equation
four consecutive integers: x, (x+1), (x+2), and (x+3)
sum them up and get 86
x + x+1 + x+2 + x+3 = 86
now solve for x, the smallest...