A dry cleaning establishment claims that a new spot remover will remove more than 70% of the spots to which it is applied. To check this claim, the spot remover will be used on 15 spots chosen at random. If fewer than 11 of the spots are removed, we shall not reject thenull hypothesis that p= 0.7; otherwise, we conclude that p > 0.7. Required:
a. Evaluate α, assuming that p = 0 .7.
b. Evaluate β for the alternative p = 0.9.

α = 1 - 0,915 = 0.085

β = 0.314

Step-by-step explanation:

Dry cleasning clain that spot remover will remove the 70% of spot. The claim support the spot and chose at random.

Null hypothesis:

H0 : p = 0.7

If 11 of spot are removed then hypothesis rejected.

If 11 spots are not removed then hypothesis accepted

H1 : p >0/7

X is the number of spot and binomial random variable.

For a)

The probability of committing the type 1 error use alpha such as

α = P ( type I error)

where X > 10

and p = 0.7

for the given values where n = 12 and r = 10 and p - 0.7

we get

α = 1 - 0,915 = 0.085

b)

The nonrejection of the hypothesis where type II error is false .

The hypothesis for this is 0.9

This is Type II error

β = P ( type II error) = P ( X <= 10 where p = 0.9 )

Where n = 12 , r = 10 and p = 0.9

then

β = 0.314

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

step-by-step explanation:

i believe its "c" because all of the other options include a but it could be d because there is a way of financing with cash at certain places but its uncommon.