Question

A college entrance exam company determined that a score of 23 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 236 on the college entrance exam 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 23 on the math portion of the exam? Complete parts a) through d) below Click the icon to view the table of critical t-values a) State the appropriate null and alternative hypotheses. Fill in the correct answers below. The appropriate null and alternative hypotheses are Ho versus H, 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. Click to select your answer(s).

a through d please

Answer 1

Given that,
population mean(u)=23
sample mean, x =23.6
standard deviation, s =3.4
number (n)=200
null, Ho: μ=23
alternate, H1: μ>23
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.653
since our test is right-tailed
reject Ho, if to > 1.653
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =23.6-23/(3.4/sqrt(200))
to =2.496
| to | =2.496
critical value
the value of |t α| with n-1 = 199 d.f is 1.653
we got |to| =2.496 & | t α | =1.653
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :right tail - Ha : ( p > 2.4957 ) = 0.00669
hence value of p0.05 > 0.00669,here we reject Ho
ANSWERS
---------------
a.
null, Ho: μ=23
alternate, H1: μ>23
b.
sample size is large than 30
test statistic: 2.496
c.
critical value: 1.653
decision: reject Ho
p-value: 0.00669
d.
we have enough evidence to support the claim that they scoring above 23 on the math portion of the exam.