For students who first enrolled in two year public institutions in a recent semester, the proportion who earned a bachelor's degree within six years was
0.3960.396.
The president of a certain college believes that the proportion of students who enroll in her institution have a
higherhigher
completion rate.
|
(a) |
Determine the null and alternative hypotheses. |
|
(b) |
Explain what it would mean to make a Type I error. |
|
(c) |
Explain what it would mean to make a Type II error. |
(a) State the hypotheses.
Upper H 0H0:
▼
muμ
pp
sigmaσ
▼
equals=
greater than>
less than<
not equals≠
nothing
Upper H 1H1:
▼
sigmaσ
pp
muμ
▼
less than<
not equals≠
greater than>
equals=
nothing
(Type integers or decimals. Do not round.)
(b) Which of the following is a Type I error?
A.The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is
0.3960.396,
when, in fact, the proportion is
0.3960.396.
B.The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is
0.3960.396,
when, in fact, the proportion is
greatergreater
than
0.3960.396.
C.The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is
0.3960.396,
when, in fact, the proportion is
0.3960.396.
D.The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is
0.3960.396,
when, in fact, the proportion is
greatergreater
than
0.3960.396.
(c) Which of the following is a Type II error?
A.The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is
0.3960.396,
when, in fact, the proportion is
greatergreater
than
0.3960.396.
B.The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is
0.3960.396,
when, in fact, the proportion is
greatergreater
than
0.3960.396.
C.The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is
0.3960.396,
when, in fact, the proportion is
0.3960.396.
D.The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is
0.3960.396,
when, in fact, the proportion is
0.3960.396.
Click to select your answer(s).
(A) it is given that the president of a certain college believes that the proportion of students who enroll in her institution have a
higher completion rate
So, null hypothesis Ho: p = 0.396
Alternate hypothesis Ha: p>0.396
(B) Type I error is rejection of a true null hypothesis, i.e. rejection of statement that the proportion is equal to 0.396, when it fact, it is actually equal to 0.396
option C is correct
(C) Type II error is the failure to reject the false null hypothesis, i.e. failing to reject the statement that proportion is equal to 0.396, when in fact, proportion is greater than 0.396
option B is correct
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