A social worker randomly selects 28 households with children. He finds a correlation of -0.21

Question 1
A social worker randomly selects 28 households with children. He finds a correlation of -0.21
between the average weekly work hours of the parents and the happiness index of the children
in that household. Is the correlation coefficient statistically significant at the 5% significance
level? Be sure to state the null and the alternative hypotheses, draw a picture of the distri-
bution, find the critical value, compute the test statistic, and state your decision. What do
you conclude? Explain briefly
Given: r=
, n=
, α=
Step 1. State the Null and the Alternative hypotheses:
H 0 :
H A :
Step 2.
The critical
-tailed
value is
test for the correlation coefficient, d.f.=
Step 3. Find the test statistic:
Step 4. Decision Rule:
Step 5. Conclusion & Explanation:
.Question 2
t-Test results have been redacted from this Stata output:
Income98 has a standard deviation of 5.49, and educ has a standard deviation of 2.89. Is the
slope statistically significant at the 5% significance level? Be sure to state the null and the
alternative hypotheses, find the critical value, compute the test statistic for the slope, and
state your decision. What can you say about the relationship between education and income?
Explain briefly.
Given:
b=
is the dependent variable (y),
, s y =
, s x =
, R 2 =
is the independent variable (x).
, n=
, α=
Step 1. State the Null and the Alternative hypotheses:
H 0 :
H A :
Step 2.
The critical
-tailed
value is
test for the
, d.f.=
Step 3. Find the test statistic:
Step 4. Decision Rule:
Step 5. Conclusion &Explanation: