Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 250 companies to invest in. After 1 year, 135 of the companies were considered winners; that is, they outperformed other companies in the same investment class. To assess whether the dart-picking strategy resulted in a majority of winners, the researcher tested Upper H 0: pequals0.5 versus Upper H 1: pgreater than0.5 and obtained a P-value of 0.1030. Explain what this P-value means and write a conclusion for the researcher.

The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance

Null hypothesis is accepted at 0.05 level of significance

The population proportion is equal to 0.5

Step-by-step explanation:

Step (i):-

Given random sample size ' n' = 250

Sample proportion 'p'

Given Population proportion  P = 0.5

                                       Q = 1-P = 1-0.5 =0.5

Null Hypothesis : H₀ : P = 0.5

Alternative Hypothesis : H₁ : P≥ 0.5

Step(ii):-

Test statistic

            Z  = 1.2903

Level of significance α = 0.05

Z₀.₀₅ = 1.96

The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance

Null hypothesis is accepted at 0.05 level of significance

Step(iii):-

P- value

The probability of test statistic

P(Z > 1.2903) = 0.5 - A ( 1.2903)

                      = 0.5 - 0.4015

                      = 0.0985≅ 0.10

i) P- value =0.10 >  α = 0.05

null hypothesis is accepted

Conclusion:-

The population proportion is equal to 0.5

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

570, the answer is 570, hope it