A college entrance exam company determined that a score of 24 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 24.5 on the college entrance exam with a standard deviation of 3.3.
a) Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 24 on the math portion of the exam?
b) State the appropriate null and alternative hypotheses.

a) The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance

Null hypothesis is accepted at  0.01% level of significance

They score is above 24 on the math portion of the exam

b)

Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school

H₀: μ = 24

Alternative Hypothesis: H₁: μ ≠ 24

Step-by-step explanation:

Step(i):-

Given random sample 'n' = 250

Given data sample mean x⁻ = 24.5

Standard deviation = 3.3

Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school

H₀: μ = 24

Alternative Hypothesis: H₁: μ ≠ 24

test statistic

a) 99% or 0.01% level of significance

Level of significance ∝ = 0.01

The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance

Null hypothesis is accepted at  0.01% level of significance

They score is above 24 on the math portion of the exam

b) 95% or 0.05% level of significance

Level of significance ∝ = 0.05

The Z -value 2.397 > 1.96 at 95% or 0.05% level of significance

Null hypothesis is Rejected at  0.05% level of significance

They score is below 24 on the math portion of the exam