# 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

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