business statistics

A recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitmentbetween two partners in a committed romantic relationship. One aspect of the study involved
47 heterosexual couples who are part of an online pool of people willing to participate in
surveys. These 47 couples were asked about which person was the first to say “I love you.” Fro
7 of those couples, the two people disagreed about the answer to this question. But both
people agreed for the other 40 couples, so those 40 responses were included in the analysis.
Previous studies have suggested that males tend to say “I love you” first.
1. Identify the observational units and variable in this study. Also classify the variable as
categorical or quantitative.
2. Stathe the appropriate null and alternative hypotheses (in words) for testing whether
males are more likely to say “I love you” first.
3. Describe what the symbol 𝜋 stands for in this context.
It turned out that for 28 of the 40 couples in the sample, the man said “I love you” before the
woman did.
4. Determine the sample proportion of couples for whom the man was the first to say “I
love you.” What symbol do we use to denote this proportion?
5. Conduct a simulation analysis to assess the strength of evidence against the null
hypothesis provided by this sample data. Provide a screenshot or report the values you
used in the applet in order to get a p-value and report the p-value.
6. Interpret the p-value in the context of this problem.
7. Summarize your conclusion based on this p-value.
8. Report the standardized statistic for this problem.
9. Interpret the standardized statistic for this problem.
10. Using a theory-based test, what is the p-value.
11. Without using an applet, what would the theory-based p-value be if we used a twosided alternative hypothesis for this study?
12. What would the hypothesis look like in “math-speak” and how would you interpret it?
MSC 300
Packet 2
Name_____________________________________
1. Suppose I hand out candy before an exam. I randomly distribute Smarties to 15
students and Dum Dums to the other 15 in class. I want to investigate whether the type
of candy students receive has an effect on their exam scores. (3 pts)
a. Identify the observational units in this study and how many there are.
b. Identify one of the variables in this study, and classify it as quantitative or
categorical.
c. Identify the other variable in this study, and classify it as quantitative or
categorical.
2. In the latest Gallup survey, they asked a random sample of adult Americans if they had a
gun in their home. Of the 1000 they surveyed 43% reported they did have a gun in their
home. Describe what each of the following are for this scenario. (2 pts)
a. Sample.
b. Population.
c. Statistic.
d. Parameter.
3. The null and alternative hypotheses are statements about values of: (1 pt)
a.
b.
c.
d.
The population parameters
The sample statistics
Both the population parameters and the sample statistics
Neither the population parameters and the sample statistics
4. The simulation (flipping coins or using the applet) done to develop the distribution we
used to find our p-values assumes which hypothesis is true? (1 pt)
a.
b.
c.
d.
Null hypothesis
Alternative hypothesis
Both hypotheses
Neither hypothesis
5. Suppose you are testing to see if your dog, Hope, understands pointing towards an
object like Harley does. You put Hope through 20 trials and 13 times (or 65%) she goes
to the correct object. You then conduct a test of significance (with H0: π = 0.5 and
Ha: π > 0.5) and generate the following simulation using an applet. (Note this null
distribution uses only 100 simulated samples and not the usual 1000 or 10,000.) (3 pts)
a) What is the value of the p-value for your test? (Also circle the dots in the null
distribution that represent the numerator of your p-value.)
b) Based on your p-value, do you have strong evidence against the null hypothesis?
(Hence, strong evidence that Hope understands pointing.)
c) What does a single dot represent in the null distribution shown above?
i) A simulation for the results of Hope completing one trail if she goes to the correct
object 50% of the time in the long run.
ii) A simulation for the results of Hope completing one trail if she goes to the correct
object more than 50% of the time in the long run.
iii) A simulation for the number of times Hope goes to the correct object out of 20 if she
goes to the correct object 50% of the time in the long run.
iv) A simulation for the number of times Hope goes to the correct object out of 20 if she
goes to the correct object more than 50% of the time in the long run.
6) Lambert and Pinheiro (2006) describe a study in which researchers try to identify
characteristics of cell phone calls that suggest the phone is being used fraudulently. For each
cell phone call, the researchers recorded the following variables:
•
•
•
•
•
call direction (incoming or outgoing)
location (local or roaming)
duration (in minutes)
day of week
whether or not the call took place on a weekend or weekday
(a) Identify the observational units in this study.
(b) Place a C next to the variables that are categorical and a Q next the variables that are
quantitative.
(c) Explain why the “average number of minutes per call” is not a valid definition of a variable for
the observational units in (a).
(d) Suppose you are told the probability of a local call is .60. Explain how you can interpret this
phrase (what is meant by “probability”?) without using the terms probability, chance, likelihood,
or odds (using what you learned in Lab 0).
7) (free point) You are told that one of these men is named Bob and one is named Tim.
Which name do you think belongs to the face on the left, Tim or Bob? (circle one)
TIM
BOB