Determine the critical value(s) of the test statistic for each of the following small sample tests for the population mean where the assumption of normality is satisfied. round your answer to four decimal places.

step 1 of 3:

left-tailed test,α=0.01,n=19

step 2 of 3:

right-tailed test ,α=0.1,n=13

step 3 of 3:

two-tailed test, α=0.05,n=17

Step 1  t  = - 2.552

Step 2 t   =  1.356

Step 3  two values     t  =  - 2.12 on the left   and   t = 2.12 on the right

Step-by-step explanation:

Normal Distribution

size sample  < 30

Table to use  t-student table

a)  left-tailed test       α  =  0,01            n = 19      gl   = 19 -1      gl = 18

Directly from  t table      

t  = - 2.552

b) Right-tailed test     α  = 0,1     n  = 13     gl  = 13 - 1    gl =12

Directly from  t table

t  = 1.356

c)  Two-tailed test   α  = 0,05   but two tails means   we use α/2

    α/2  =  0,025    n = 17   gl  = n - 1   gl  = 17  -1     gl  = 16

From table:

t =  - 2.12  on the left tail  and  t = 2.12 on the right tail

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

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )