The toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (a) under a normal load. a sample of nine motors was tested, and it was found that the mean current was x = 1.32 a, with a sample standard deviation of s = 0.44 a.

do the data indicate that the toylot claim of 0.8 a is too low? (use a 1% level of significance.)

The data indicate that toylot claim   t(s)  =  -  3,54

Step-by-step explanation:

T student distribution

sample size   n  = 9      df =  n  -  1    df  =  9  -  1    df  = 8

sample mean     μ  =  1.32

sample standard deviation     σ   =  0,44

1.- Test  hypothesis      

H₀           null hypothesis        μ₀  =    0,8

Hₐ   alternative hypothesis    μ₀  <    0,8

2.- Critical value

Confidence interval   99 %        α  =  0,01    and  df  =  8

t(c)  = - 2.8965      

3.-Compute t(s)

t(s)  =  [  (  μ  -   μ₀  ) / s/√n ]     t(s)  =  - 0,52 * 3/ 0,44      t(s)  = - 3.54

4.- Compare  t(s)   and  t(c)

t(s) is far away in the rejection region. The data indicate that toylot claim is too low  

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