A statistics practitioner in a large university is investigating the factors that affect salary of professors. He wondered if evaluations by students are related to salaries. To this end, he collected 100 observations on:

y = Annual salary (in dollars)
x = Mean score on teaching evaluation

To accomplish his goal, he assumes the following relationship:

y = β(0) + β(1)x + ε

Then, using Data Analysis, he obtained the following result.
R2=0.23

Coefficient Standard Error
Intercept 25675.5 11393
x 5321 2119

Required:
What are the null and alternative hypotheses, respectively?

Complete Question

The complete question is shown on the first uploaded image  

The null hypothesis is  

 The alternative hypothesis is  

Step-by-step explanation:

From the question we are told that

       The number observations is  

        The  annual salary (in dollars) is  y

         The  mean score on teaching evaluation is  x

         The the relationship between the y and  x is

From this mathematical relationship we see that    is the mean                

So

 The null hypothesis is    [i.e  evaluations does not affect salary]

  The alternative hypothesis is   [ i.e evaluations  affect salary ]

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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