Question

A college entrance exam company determined that a score of 21 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 200 students who completed this core set of courses results in a mean math score of 21.8 on the college entrance exam with a standard deviation of 3.5. Do these results suggest that students who complete the core curriculum are ready for​ college-level mathematics? That​ is, are they scoring above 21 on the math portion of the​ exam?

What are the appropriate null and alternative hypotheses?

Verify that the requirements to perform the test using the t-distribution are satisfied.

Use the​ P-value approach at the α=0.10 level of significance to test the hypotheses in part​ (a). Identify the test statistic.

Identify the P value.

Write a conclusion based on the results.

Answer 1

Here using ti-83 calculator.

Given a sample standard deviation (Sx).

Here unknown population standard deviation (sigma) so we can use t- distribution.

Test Hypothesis :-

H0 :

Ha :

Test statistic :-

t = 3.232

P-value :-

P=0.0007

Conclusion :-

P-value is less than alpha = 0.10, then conclude that reject the null hypothesis (H0).

Therefore, there is sufficient evidence to support the claim.