Question

In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% (The Working Poor Families Project, 2011). Although it has remained slow, some politicians now claim that the recovery from the Great Recession has been steady and noticeable. As a result, it is believed that the national percent of low-income working families is significantly lower now in 2014 than it was in 2011. To support this belief, a recent spring 2014 sample of n=16 jurisdictions produced a sample mean of 29.8% for the percent of low income working families, with a sample standard deviation of 4.1%. Using a 0.10 significance level, test the claim that the national average percent of low-income working families has improved since 2011.

8. Write a few brief sentences to state the type of test that should be performed (Student t-test or z-test – i.e. what type of data do you have? Categorical or quantitative? Discuss. Is this is a left, right or two tailed test? How do you know? Explain thoroughly.)

9. Write the assumptions and conditions of the test that justify its appropriateness.

10. Clearly identify and state the null and alternate hypothesis for this test.

11. Use technology to identify the p-value associated with the hypothesis test.

12. State the decision of the hypothesis test based on a 0.10 significance level.

13. Provide the appropriate conclusion about the claim that the national average percent of low income working families has improved since 2011.

Answer 1

Given that,
population mean(u)=31.3
sample mean, x =29.8
standard deviation, s =4.1
number (n)=16
null, Ho: μ=31.3
alternate, H1: μ<31.3
level of significance, α = 0.1
from standard normal table,left tailed t α/2 =1.341
since our test is left-tailed
reject Ho, if to < -1.341
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =29.8-31.3/(4.1/sqrt(16))
to =-1.4634
| to | =1.4634
critical value
the value of |t α| with n-1 = 15 d.f is 1.341
we got |to| =1.4634 & | t α | =1.341
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :left tail - Ha : ( p < -1.4634 ) = 0.082
hence value of p0.1 > 0.082,here we reject Ho
ANSWERS
---------------
8.
t test with unknown population standard deviation
9.
standard t test distribution
10.
null, Ho: μ=31.3
alternate, H1: μ<31.3
11.
test statistic: -1.4634
critical value: -1.341
12.
decision: reject Ho
p-value: 0.082
13.
we have enough evidence to support the claim that the national average percent of low-income working families has improved since 2011.