Question

A college entrance study company determined that a score of

20

on the mathematics portion of the study 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

150

students who completed this core set of courses results in a mean math score of

20.3

on the college entrance study with a standard deviation of

3.4

Do these results suggest that students who complete the core curriculum are ready for​ college-level mathematics? That​ is, are they scoring above

20

on the math portion of the​ study? 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​:

▼

muμ

x overbarx

▼

greater than or equals≥

equals=

less than or equals≤

less than<

greater than>

nothing versus

H1​:

▼

x overbarx

muμ

▼

less than or equals≤

greater than>

less than<

greater than or equals≥

equals=

nothing.

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

C.

The sample size is larger than 30.

D.

None of the requirements are satisfied.

​c) Use the​ P-value approach at the

alphaαequals=0.05

level of significance to test the hypotheses in part​ (a).

Identify the test statistic.

t 0t0

equals=

nothing ​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

​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

20

Answer 1