The average score of all high school students in math and science is 150 with a standard deviation of 25. A random sample of 125 students in a district shows an average score of 158. At 95%, is the difference significant? Follow the five-step one-sample test and write your conclusion.

The difference is significative we reject H₀

Step-by-step explanation:

Normal Distribution

Population mean            X₁    =  150

Population standard deviation       σ  =  25

Sample size        n   =  125

Sample mean     X₂   =  158

1.-CI =  95 %   significance level    α  =  5%    α = 0,05

From z-table α = 0,05    z(c)  =   1,64    ( the test is one-tail test to the right)

2.-Hypothesis Test

Null Hypothesis                                    H₀        X₂  =  X₁

Alternative Hypothesis                        Hₐ        X₂  >  X₁

3.-To compute z(s)

z(s)  =  ( X₂  -  X₁ ) / σ/√n

z(s)  =    8 * 11,14 /25

z(s)  =  89,12/25

z(s)  = 3,56

4.- Comparing  z(s)  and z(c)

z(s)  > z(c)

Then z(s) is in the rejection region we reject H₀

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!

(-infinity,infinity)