State the null and alternative hypotheses to test if the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2. Let µd be the population mean of​ matched-pair differences for Sample 1 - Sample 2. State the null and alternative hypotheses. Pair 1 2 3 4 5 6 7
Sample1 5 6 10 3 6 7 8
Sample2 4 4 3 5 5 5 3

Null Hypothesis, : = 2.0 units  or   = 2.0 units

Alternate Hypothesis, : 2.0 units  or   2.0 units

Step-by-step explanation:

We are given the following data below and we have test if the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2;

Pair : 1 2 3 4 5 6 7

Sample1 : 5 6 10 3 6 7 8

Sample2 : 4 4 3 5 5 5 3

Let = population mean represented by Sample 1

= population mean represented by Sample 2

= population mean matched-pair differences for Sample 1 - Sample 2

So, Null Hypothesis, : = 2.0 units  or   = 2.0 units

Alternate Hypothesis, : 2.0 units  or   2.0 units

Here null hypothesis states that the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2.

On the other hand, alternate hypothesis states that the population represented by Sample 1 has a mean that is not 2.0 units higher than the population represented by Sample 2.

i am chris from the united states i have skill in math and i am here to evryone

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24