Question

You want to test whether salaries have gone up compared to the year 2000. The 2000 Census shows that the average annual salary of all Americans was $35,152. You take an SRS of 10 Americans, ask for their annual salary for the year, and get the following results in thousands of dollars:

Annual Salary
45
16
24
83
103
31
69
94
72
20

A) Determine the population(s) and parameter(s) being discussed.

B) Determine which tool will help us find what we need (one sample z test, one sample t test, two sample t test, one sample z interval, one sample t interval, two sample t interval).

C) Check if the conditions for this tool hold.

D) Whether or not the conditions hold, use the tool you choose in part B. Use C=95% for all confidence intervals and alpha=5% for all significance tests.

* Be sure that all methods end with a sentence describing the results *

Answer 1

A.
Given that,
population mean(u)=35152
sample mean, x =55700
standard deviation, s =32441.5714
number (n)=10
null, Ho: μ=35152
alternate, H1: μ!=35152
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.262
since our test is two-tailed
reject Ho, if to < -2.262 OR if to > 2.262
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =55700-35152/(32441.5714/sqrt(10))
to =2.0029
| to | =2.0029
critical value
the value of |t α| with n-1 = 9 d.f is 2.262
we got |to| =2.0029 & | t α | =2.262
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.0029 ) = 0.0762
hence value of p0.05 < 0.0762,here we do not reject Ho
ANSWERS
---------------
B.
t test for single mean because given sample standard deviation
C.
null, Ho: μ=35152
alternate, H1: μ!=35152
test statistic: 2.0029
critical value: -2.262 , 2.262
D.
decision: do not reject Ho
p-value: 0.0762
we do not have enough evidence to support the claim that the average annual salary of all Americans was $35,152.