Question

A college entrance exam company determined that a score of 22 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 22.5 on the college entrance exam with a standard deviation of 3.9.

Verify that the requirements to perform the test using the​ t-distribution are satisfied. Check all that apply.

A. The​ students' test scores were independent of one another.

B. The sample size is larger than 30.

C. The students were randomly sampled.

D. None of the requirements are satisfied.

Answer 1

(a)

It is verified that the requirements to perform the test using the​ t-distribution are satisfied.

A. The​ students' test scores were independent of one another.

C. The students were randomly sampled.

(b)

H0: Null Hypothesis: 22

HA: Alternative Hypothesis: 22

SE = s/

= 3.9/

= 0.2467

Test Statistic is given by:

t = (22.5 - 22)/0.2467

= 2.0271

Take = 0.05

ndf = 250 - 1 = 249

From Table, critical value of t = 1.6510

Since calculated value of t is greater than critical value of t, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that students are ready for​ college-level mathematics by achieving the goal of a score of 22 on the mathematics portion of the exam.