Question

You want to test whether salaries have gone up compared to in the year 2000. The 2000 census shows that the average annual salary of all Americans in 2000 was $35,152. You take an SRS of 10 Americans, ask for their annual salary for this 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, two sample t intervals)

c) Check if the conditions for this tool hold

d) Whether or not the conditions hold, use the tool you chose in part (b) . Use C=95% for all confidence intervals and a=5% for all significance tests.

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

Answer 1

a) Determine the population(s) and parameter(s) being discussed

population: annual salary of all Americans in 2000

parameter:  average annual salary of all Americans ,mu=35152

Soluiton-b:

since population standard deviation i not given

and sample size ,n=10

perform t test for mean

ANSWER;

one sample t test

Solution-c:

here n=10

simle random sample

Its not given sample follows normal distribution

Conditions are not met

d) Whether or not the conditions hold, use the tool you chose in part (b) . Use C=95% for all confidence intervals and a=5% for all significance tests.

Ho:mu=35152

Ha:mu >35152

alpha=0.05

t=xbar-mu/s.sqrt(n)

Fro the given sample

n=10

sample mean=xbar= 55700

sample standard deviation=s=32441.57

t=(55700-35152)/(32441.57/sqrt(10)

t=2.002939
df=n-1=10-1=9

p value in excel

=T.DIST.RT(2.002939,9)

=0.038095

p<0.05

Reject Ho

Accept Ha

Conclusion:

There is suffcient evidence at 5% level of signfiicance to conlcude that salaries have gone up compared to in the year 2000.