In 1996, 31% of elementary students reported that their mothers had graduated fr
ID: 3434197 • Letter: I
Question
In 1996, 31% of elementary students reported that their mothers had graduated from college. In 2000, responses from 8368 found that this figure grown to 32%. Is this evidence of a change in education level among mothers?
a. Define the population proportion of interest.
b. State hypothesis
c. check conditions
d. Find the test statistics
e. Find the P-value
f. Do you reject or fil to reject Ho at the .05 significance level?
g. Make a condition in the context of the original problem.
h. What type of error could you have made?
i. Is this change significant practically?
Explanation / Answer
a. Define the population proportion of interest.
All elementary students reported that their mothers had graduated from college
-------------------------------------------------------------------------------------------------------
b. State hypothesis
Ho: p=0.31 (i.e. null hypothesis)
Ha: p not equal to 0.31 (i.e. alternative hypothesis)
-------------------------------------------------------------------------------------------------------
c. check conditions
We need to assume that the population follows Normal distribution
-------------------------------------------------------------------------------------------------------
d. Find the test statistics
Z=(phat-p)/sqrt(p*(1-p)/n)
=(0.32-0.31)/sqrt(0.31*(1-0.31)/8368)
=1.98
-------------------------------------------------------------------------------------------------------
e. Find the P-value
It is a two-tailed test.
So the p-value= 2*P(Z>1.98) = 0.0477 (from standard normal table)
-------------------------------------------------------------------------------------------------------
f. Do you reject or fil to reject Ho at the .05 significance level?
Since the p-value is less than 0.05, we reject Ho.
-------------------------------------------------------------------------------------------------------
g. Make a condition in the context of the original problem.
So we can conclude that this is evidence of a change in education level among mothers
-------------------------------------------------------------------------------------------------------
h. What type of error could you have made?
Type I error.
We reject Ho when it is true.
-------------------------------------------------------------------------------------------------------
i. Is this change significant practically?
Yes.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.