In: Statistics and Probability
1.
In a certain school district, it was observed that 30% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 136 out of 392 students are only children. The
school district administrators want to know if the proportion of
only children in the special program is significantly different
from the proportion for the school district. Test at the α=0.02
level of significance.
What is the hypothesized population proportion for this test?
p=
(Report answer as a decimal accurate to 2 decimal places. Do
not report using the percent symbol.)
Based on the statement of this problem, how many tails would this
hypothesis test have?
Choose the correct pair of hypotheses for this situation:
(A) | (B) | (C) |
---|---|---|
H0:p=0.3 |
Ha:p<0.3
H0:p=0.3 |
Ha:p≠0.3
H0:p=0.3 |
Ha:p>0.3
(D) | (E) | (F) |
---|---|---|
H0:p=0.347 |
Ha:p<0.347
H0:p=0.347 |
Ha:p≠0.347
H0:p=0.347 |
Ha:p>0.347
(A)
(B)
(C)
(D)
(E)
(F)
Using the normal approximation for the binomial distribution
(without the continuity correction), what is the test statistic for
this sample based on the sample proportion?
z=
(Report answer as a decimal accurate to 3 decimal
places.)
You are now ready to calculate the P-value for this sample.
P-value =
(Report answer as a decimal accurate to 4 decimal
places.)
This P-value (and test statistic) leads to a decision to...
As such, the final conclusion is that...
2.
In a certain school district, it was observed that 29% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 122 out of 374 students are only children. The
school district administrators want to know if the proportion of
only children in the special program is significantly different
from the proportion for the school district. Test at the α=0.01
level of significance.
What is the hypothesized population proportion for this test?
p=
(Report answer as a decimal accurate to 2 decimal places. Do
not report using the percent symbol.)
Based on the statement of this problem, how many tails would this
hypothesis test have?
Choose the correct pair of hypotheses for this situation:
(A) | (B) | (C) | H0:p=0.29 |
---|
Ha:p<0.29
H0:p=0.29 |
Ha:p≠0.29
H0:p=0.29 |
Ha:p>0.29
(D) | (E) | (F) | H0:p=0.326 |
---|
Ha:p<0.326
H0:p=0.326 |
Ha:p≠0.326
H0:p=0.326 |
Ha:p>0.326
(A)
(B)
(C)
(D)
(E)
(F)
Using the normal approximation for the binomial distribution
(without the continuity correction), was is the test statistic for
this sample based on the sample proportion?
z=
(Report answer as a decimal accurate to 3 decimal
places.)
You are now ready to calculate the P-value for this sample.
P-value =
(Report answer as a decimal accurate to 4 decimal
places.)
This P-value (and test statistic) leads to a decision to...
As such, the final conclusion is that...
1. There is no sufficient evidence to support the assertion that the proportion of only children in the special program is significantly different from the proportion for the school district.
2. There is no sufficient evidence to support the assertion that the proportion of only children in the special program is significantly different from the proportion for the school district.