Question

A college entrance test company determined that a score of

21

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

150

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

21.4

on the college entrance test 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

21

on the math portion of the​ test? Complete parts​ a) through​ d) below.

a) State the appropriate null and alternative hypotheses.

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

​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.

Identify the​ P-value.

​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 not

is

sufficient evidence to conclude that the population mean is

▼

less

greater

than

21.

Answer 1

Answer:

n= 150,  = 21

= 21.4 , s = 3.4

= 0.05

a)

null and alternative hypothesis is

Ho:   = 21

H1:   > 21

b)

- The students were randomly sampled.

-The sample size is larger than 30.

-The students test scores were independent of one another.

c)

formula for test statistics is

t = 1.44088

to = 1.44

now calculate P-Value for this one tailed test with df= n-1 = 150-1 = 149, using following

excel command we get p-value as,

P-Value = 0.076

decision rule is,

Reject Ho if (P-Value) < ( )

Here, ( P-Value = 0.076) > ( = 0.05 )

Hence,

Null hypothesis is NOT rejected.

d)

Do not reject the null hypothesis and claim that there is not sufficient evidence to conclude that the population mean is greater than 21