21 - Colorado Mesa University
HW # 10 – HT and CI for one proportion
Note that for each problem parts C through G are:
C) Give the critical value(s) (from the table).
D) Give the value of the test statistic (from the data).
E) Is the answer Yes or No?
F) What is the p-value?
G) Describe the meaning of the p-value in everyday terms.
Also all sample data are given at the end of the assignment.
1. (IN CLASS) Can we prove the percentage of all students that are from out of state for University A is below 10%?
A) Before collecting data what is the chance of concluding the percentage is below 10% when it isn’t?
B) Before collecting data what is the chance of not concluding the percentage is below 10% when it actually is?
H) Give a 95% CI for the percentage of out of state students at University A.
I) Estimate how large a sample is needed to ensure the margin of error in a 95% CI is 3% if you trust the initial data?
J) How large a sample is needed to ensure the margin of error in a 95% CI is 3% if you don’t have any data collected yet?
2. (IN CLASS) Can we prove that the percentage of all students that are from out of state is not 10% for University A? Just answer parts C through F.
3. (ANSWER GIVEN) Can we prove at the 1% level of significance that the percentage of all students that are from out of state for University B is over 10%?
A) Before collecting data what is the chance of concluding the percentage is below 10% when it isn’t?
B) Before collecting data what is the chance of not concluding the percentage is below 10% when it actually is?
H) Give a 99% CI for the percentage of out of state students at University B.
I) Estimate how large a sample is needed to ensure the margin of error in a 99% CI is 3% if you trust the initial data?
J) How large a sample is needed to ensure the margin of error in a 99% CI is 3% if you don’t have any data collected yet?
4. (ANSWER GIVEN) Can we prove at the 1% level of significance that the percentage of all students that are from out of state is not 10% for University B? Just answer parts C through F.
5. (SOLUTION GIVEN) Can we prove at the 10% level of significance that the percentage of all students that are from out of state for University C is over 10%?
A) Before collecting data what is the chance of concluding the percentage is over 10% when it isn’t?
B) Before collecting data what is the chance of not concluding the percentage is over 10% when it actually is?
H) Give a 90% CI for the percentage of out of state students at University C.
I) Estimate how large a sample is needed to ensure the margin of error in a 90% CI is 3% if you trust the initial data?
J) How large a sample is needed to ensure the margin of error in a 90% CI is 3% if you don’t have any data collected yet?
6. (SOLUTION GIVEN) Can we prove at the 10% level of significance that the percentage of all students that are from out of state is not 10% for University C? Just answer parts C through F.
7. (HOMEWORK) Can we prove at the 1% level of significance that the percentage of all credit card accounts in Nevada that have over 1000$ balance after the last payment is over 40%?
A) Before collecting data what is the chance of concluding the percentage is over 40% when it isn’t?
B) Before collecting data what is the chance of not concluding the percentage is over 40% when it actually is?
H) Give a 99% CI for the percentage of all credit card accounts from Nevada that had over 1000$ balance after the last payment.
I) Estimate how large a sample is needed to ensure the margin of error in a 99% CI is 3% if you trust the initial data?
J) How large a sample is needed to ensure the margin of error in a 99% CI is 3% if you don’t have any data collected yet?
8. (HOMEWORK) Can we prove at the 1% level of significance that the percentage of all credit card accounts in Nevada that have over 1000$ balance after the last payment is not 40%? Just answer parts C through F.
9. (ALTERNATE HW) Can we prove at the 5% level of significance that the percentage of all credit card accounts in Colorado that have over 1000$ balance after the last payment is below 40%?
A) Before collecting data what is the chance of concluding the percentage is over 40% when it isn’t?
B) Before collecting data what is the chance of not concluding the percentage is over 40% when it actually is?
H) Give a 95% CI for the percentage of all credit card accounts from Colorado that had over 1000$ balance after the last payment.
I) Estimate how large a sample is needed to ensure the margin of error in a 95% CI is 3% if you trust the initial data?
J) How large a sample is needed to ensure the margin of error in a 95% CI is 3% if you don’t have any data collected yet?
10. (ALTERNATE HW) Can we prove at the 5% level of significance that the percentage of all credit card accounts from Colorado that have over 1000$ balance after the last payment is not 40%? Just answer parts C through F.
Data:
1, 2, 3, 4, 5, 6 SRS’s of students at each University
| |University A |University B |University C |
|Out of State |18 |29 |28 |
|In State |230 |180 |200 |
7, 8, 9, 10 SRS’s of credit card accounts
| |Nevada |California |Colorado |
|How many with over 1000$ balance after last payment |512 |555 |560 |
|Total number of accounts in sample |1200 |1400 |1500 |
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