Question

A college entrance test company determined that a score of 25 on the mathematics portion of the test 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 25.7 on the college entrance test with a standard deviation of 3.3. Do these results suggest that students who complete the core curriculum are ready for​ college-level mathematics? That​ is, are they scoring above 25 on the math portion of the​ test? 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' 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.

​c) Use the classical approach at the alpha=0.10 level of significance to find the critical value and test the hypotheses. Identify the test statistic.

Identify the critical value. Select the correct choice below and fill in the answer box within your choice.

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

(Reject,Do not reject) the null hypothesis and claim that there (is is not) sufficient evidence to conclude that the population mean is (greater,less than)

25.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 25
Alternative Hypothesis, Ha: μ > 25

b)

B.

The sample size is larger than 30.

C.

The students were randomly sampled.

c)

Rejection Region
This is right tailed test, for α = 0.1 and df = 199
Critical value of t is 1.286.
Hence reject H0 if t > 1.286

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (25.7 - 25)/(3.3/sqrt(200))
t = 3

d)

(Reject,) the null hypothesis and claim that there (is ) sufficient evidence to conclude that the population mean is (greater)

25.