Question

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 200 students who completed this core set of courses results in a mean math score of 24.3 on the college entrance exam with a standard deviation of 3.6.

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? Complete parts​ a) through​ d) below.

a) State the appropriate null and alternative hypotheses. Fill in the correct answers below.

The appropriate null and alternative hypotheses are H0​:_____ ______ _____ H1​: ______ _______ _____

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

A. The students were randomly sampled.

B. The sample size is larger than 30.

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

D. None of the requirements are satisfied.

​c) Use the​ P-value approach at the a=0.05 level of significance to test the hypotheses in part​ (a).

Identify the test statistic.

t0

=

_________​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=________ ​(Round to three decimal places as​ needed.)

​d) Write a conclusion based on the results. Choose the correct answer below.

_________the null hypothesis and claim that there _________sufficient evidence to conclude that the population mean is __________than 24.

Answer 1