MATH 116 - TAKE HOME ASSIGNMENT – CHAPTERS 8 & 9
Problem 1
(1) DEFINE BOTH POPULATIONS AND THE VARIABLE UNDER
CONSIDERATION
Population 1 - 30-40 year olds who do not exercise regularly
Population 2 - 30-40 year olds who exercise regularly
Variable: Resting pulse rate
(2) Write the SUMMARY STATISTICS
(3) FIND THE POINT ESTIMATE and THINK AS A SCIENTIST
Our samples indicate that the resting pulse rate is higher for people who DNER
Is it higher by chance or significantly higher? The p-value will tell us the likelihood of
such a results or a more extreme one.
(4) WRITE BOTH HYPOTHESIS, GRAPH, SHADE, LABEL
(5) USE A FEATURE OF THE CALCULATOR TO TEST THE HYPOTHESIS –
WRITE RESULTS
The p-value indicates that a point estimate of 4 is a likely event.
At the 5% significance level, the samples do not provide enough evidence to support the
claim that people who do not exercise regularly have a higher resting pulse than people
who exercise regularly.
Problem 2) a) Use the data from problem 1 to construct a 90% confidence interval estimate
for the difference between the resting pulse rate of people who do not exercise regularly and
people who exercise regularly from the 30-40 age group.
Do the problem completely with the calculator; specify the feature used and the results.
Indicate the point estimate, the confidence interval, and the margin of error.
b) Complete the following:
The obtained interval provides plausible values for ..............................
We are ..............% confident that the difference between the resting pulse rate of people
who do not exercise regularly and people who exercise regularly from the 30-40 age
group...........is somewhere between ...........................and.........................
c) What does the interval suggest? Circle the correct choices below:
u1 < u2
YES
NO
u1 may be equal to u2
YES
NO
u1 > u2
YES
NO
Very clearly explain your choice.
Since the interval contains zero, the mean resting pulse of both populations may be equal
d) Are the results of the interval consistent with the hypothesis testing result?
YES
NO
Problem 3
(1) DEFINE BOTH POPULATIONS AND THE VARIABLE/ SUCCESS ATTRIBUTE
Population 1 – people vaccinated with the drug
Population 2 – people vaccinated with a placebo
Success Attribute: Develop the disease
(2) Write the SUMMARY STATISTICS
(3) FIND THE POINT ESTIMATE and THINK AS A SCIENTIST
Our samples indicate that the proportion of people who develop the disease is lower in the
group that receives the actual vaccine. We wonder, is it lower by chance or significantly
lower? The p-value will tell us the likelihood of such a result or a more extreme one.
(4) WRITE BOTH HYPOTHESIS, GRAPH, SHADE, LABEL
(5) USE A FEATURE OF THE CALCULATOR TO TEST THE HYPOTHESIS –
WRITE RESULTS
The p-value indicates that a point estimate of -.001 is a likely event at the 2% significance
level.
At the 2% significance lever the samples do not provide enough evidence to support the
claim that the proportion of people who develop the disease is lower in the group that
receives the actual vaccine. We can’t conclude that the vaccine is effective in lowering the
incidence of the disease.
Problem 4
a) Use the calculator to find the interval. Write all answers as percents with one decimal
place.
The observed difference between sample proportions is________%__
The 96% confidence interval is (__________%, _________%)
The margin of error is ___________% (Use the interval to obtain this. Show work!)
b) What does the interval suggest? Circle the correct choices below:
p1 < p2
YES
NO
p1 may be equal to p2
YES
NO
p1 > p2
YES
NO
Very clearly explain your choice.
Since the interval contains zero, the proportion of people who develop the disease may be
equal for both populations
c) Does the interval suggest that the vaccine is effective in lowering the incidence of the
disease?
We can’t conclude that the vaccine is effective in lowering the incidence of the disease.
Problem 5
(1) DEFINE BOTH POPULATIONS AND THE VARIABLE UNDER
CONSIDERATION
Population 1 – Students from college A
Population 2 – Students from college B
Variable: GPA
(2) Write the SUMMARY STATISTICS
(3) FIND THE POINT ESTIMATE and THINK AS A SCIENTIST
Our samples indicate that the GPA of the students in college A is lower than the GPA of
students in college B
Is it lower by chance or significantly lower? The p-value will tell us the likelihood of such
a results or a more extreme one.
(4) WRITE BOTH HYPOTHESIS, GRAPH, SHADE, LABEL
(5) USE A FEATURE OF THE CALCULATOR TO TEST THE HYPOTHESIS –
WRITE RESULTS
The p-value indicates that a point estimate of -0.401 is an unlikely event at the 5% SL.
At the 5% significance level, the samples provide enough evidence to support the claim
that the students from college A have a lower GPA than students from college B.
Problem 5 – continued
b) USE THE DATA FROM THE LAST PROBLEM
Determine a 90% confidence interval for the difference,
between the mean GPA
of all college A students and the mean GPA of all college B students.
USE THE DATA OPTION IN YOUR CALCULATOR
The observed difference between the sample means is____________
The 90% confidence interval is ______________________________
The point estimate for the difference between the two population means is ________
The margin of error is _____________
c) Write the interpretation: We are 90% confident that
d) What does the interval suggest? Circle the correct choices below:
u1 < u2
u1 may be equal to u2
u1 > u2
YES
YES
NO
NO
YES
NO
Very clearly explain your choice.
The interval provides plausible values for
zero, it indicates that
. Since the interval is completely below