Question

Answer the questions below using the appropriate statistical technique. For questions involving the use of hypothesis testing, you must:

1. State the null and research hypotheses

2. Provide the Z(critical), T(critical), or χ 2 (critical) score corresponding to the α threshold for your test

3. Provide your test statistic

4. Provide your decision about statistical significance

An advantage that often comes with a basic knowledge of statistics is a change in salary. To see whether this was the case for Tulane University graduates, you took a random sample of 57 students who completed a statistics class and asked about their starting salaries (in thousands) after graduation. The sample had a mean of 53.3 with a standard deviation of 3.72 (i.e., x = 53.3 and s = 3.72). A call to the Office of the Registrar indicates that the average starting salary value for all Tulane students is 47.1. Do students who take statistics courses earn an equal salary compared to Tulane students generally? Use α = 0.001.

Answer 1

Given that,
population mean(u)=47.1
sample mean, x =53.3
standard deviation, s =3.72
number (n)=57
null, Ho: μ=47.1
alternate, H1: μ!=47.1
level of significance, α = 0.001
from standard normal table, two tailed t α/2 =3.473
since our test is two-tailed
reject Ho, if to < -3.473 OR if to > 3.473
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =53.3-47.1/(3.72/sqrt(57))
to =12.5831
| to | =12.5831
critical value
the value of |t α| with n-1 = 56 d.f is 3.473
we got |to| =12.5831 & | t α | =3.473
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 12.5831 ) = 0
hence value of p0.001 > 0,here we reject Ho
ANSWERS
---------------
1.
null, Ho: μ=47.1
alternate, H1: μ!=47.1
2.
critical value: -3.473 , 3.473
3.
test statistic: 12.5831
4.
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that students who take statistics courses earn an equal salary
compared to Tulane students generally.