Microsoft Word - Exam 4 OL Sp2020 Math12.docx
Math 12OL Name___________________________________
Spring 2020
Exam Score: _____________
Exam 3
For problems 1-7, circle the letter next to the response that best answers the question or completes the sentence. You
do not have to show any work or write any explanations here.
Make sure to read each statement carefully! XXXXXXXXXXpts each)
1. The null hypothesis ( 0H ) is a claim about a:
A) statistic, where the claim is assumed to be false until it is declared true
B) statistic, where the claim is assumed to be true until it is declared false
C) parameter, where the claim is assumed to be true until it is declared false
D) parameter, where the claim is taken to be false until it is declared true
2. If we get a p-value of 0.011 in a hypothesis test with 2% significance level, then we would
A) REJECT the null hypothesis
B) NOT REJECT the null hypothesis
C) not know whether or not to reject unless we knew if it was a one or two tailed test
D) not know whether or not to reject unless we knew the sample size
3. In a hypothesis test, the p-value is:
A) the probability of rejecting the null hypothesis when the null hypothesis is true
B) the probability of not rejecting the null hypothesis when the alternative hypothesis is true
C) the probability of selecting a sample whose test statistic is at least as extreme as the observed test
statistic that we got, assuming the null hypothesis is true
D) the probability of selecting a sample whose test statistic is at least as extreme as the observed test
statistic that we got, assuming the null hypothesis is false
4. We randomly select 20 couples and compare the time the husbands and wives spend watching TV. This
is an example of
A) independent samples
B) paired samples
C) none of the above
5. If we fail to reject 0H , then
A) we know for certain that 0H is true
B) we know for certain that 0H is false
C) it is an indication that 0H may be true
6. When constructing a 95% confidence interval for the average math test score difference between all
students at two different colleges (Beach College average test scores minus Ca
illo College average
test scores), our calculator gives us the interval ( -4.6 , XXXXXXXXXXThis can be interpreted as
A) we are 95% confident that Ca
illo College students score between 2.1 and 4.6 points more than
Beach College students, on average.
B) we are 95% confident that Ca
illo College students score between 2.1 and 4.6 points less than
Beach College students, on average.
C) we don’t know for certain that it’s a difference in the average math scores since our confidence
interval contains 0.
D) it is impossible to interpret an interval for a difference of two population means.
7. You can na
ow the width of a confidence interval by:
A) lowering the confidence level or decreasing the sample size
B) lowering the confidence level or increasing the sample size
C) increasing the confidence level or decreasing the sample size
D) increasing the confidence level or increasing the sample size
8. 10% of all Americans don’t use internet (April XXXXXXXXXXA rural town wants to know if their citizens
tend to use internet less than the country average. Suppose we want to test this claim at a 1%
significance level XXXXXXXXXXpts)
a) State what your null and alternative Hypotheses would be
0H : ____________________ 1H : ____________________
) If our conclusion is that there is not sufficient evidence to show the citizens of this town uses
internet less than the national average, but the truth is that they do, then we have made a
A) type I e
or B) type II e
or C) co
ect decision
9. A simple random sample of 28 students was taken at Ca
illo, and they found that 12 of them owned
a pet. Are all the assumptions
equirements met so that we could test the claim that more than 30%
of all students at Ca
illo owns a pet? Explain why or why not XXXXXXXXXXpts)
10. A study of the weight difference before and after being on Atkins diet for one year, showed that the
average weight loss was between 0.56 and 3.64 lbs XXXXXXXXXX4pts)
a) Find the point estimate
) Find the margin of e
or
11. In a hypothesis of the mean using the t-distribution, we got a sample mean with a test statistics
t = 2.5. The picture of the co
esponding t-curve is shown below, with the area in the right tail
calculated (area = XXXXXXXXXX).
(a) Find the p-value if we are testing
0H : ? = 22
?# : ? > 22
(b) Find the p-value if we are testing
0H : ? = 22
?#: ? ≠22
For problems 12-15 you need to show all work in order to receive credit! Make sure to clearly state
what parameters, formulas and calculator programs you are using. Make sure to use co
ect
symbols!
Write your answer using a complete sentence with co
ect units that indicates that you fully
understand the answer.
12. An analysis of the blood of 3,300 people living in Santa Clara county in early April found that 50
of them tested positive for COVID-19 antibodies (indicating that they have prior been infected by the
Corona virus). Test the claim that more than 1% of Santa Clara’s population have been infected by the
Corona. (We will assume that these test results were co
ect, which is somewhat disputable at this
point still). Use a 2% significance level XXXXXXXXXX14pts)
1. State the null and alternate hypotheses.
2. State the significance level.
3. Compute the test statistic (by hand).
4. Calculate the p-value.
5. Compare p-value with α and make a decision.
6. Clearly state your conclusion as a full sentence.
13. In a random sample of 31 people who were playing the slot machines the mean age was 48.7 years
with a standard deviation of 6.8. In a random sample of 35 people who were playing roulette the mean
age was 51.3 years with a standard deviation of 3.2.
Use a 1% significance level to test the claim that the average age of those playing the slot machines are
younger than those playing roulette XXXXXXXXXX14pts)
1. State the null and alternate hypotheses.
2. State the significance level.
3. Find the test statistic.
4. Find the p-value.
5. Compare p-value with α and make a decision.
6. Clearly state your conclusion as a full sentence.
14. A researcher wanted to estimate the affect a new drug would have on systolic blood pressure. The
following table gives the systolic blood pressures (in mm Hg) of seven adults before taking this
drug, and after having taken this drug for 2 months.
Before XXXXXXXXXX XXXXXXXXXX
After XXXXXXXXXX XXXXXXXXXX
We will assume that the population of paired differences is approximately normally distributed. (12pts)
Construct a 90% confidence interval for the difference in systolic blood pressure before and after
taking this drug.
1. Find the point estimate
2. Find the critical value (you can skip this step if you want to)
3. Find the standard e
or and the margin of e
or (you can skip this step if you want to)
4. Find the confidence interval
5. Interpret your result. Clearly state which is more or less, and by how much.
15. A researcher is designing an experiment in which rats will navigate a maze. The average time it
takes a white rat to complete the