Stats_13_Homework_1_
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University of California, Los Angeles *
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Course
13
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
5
Uploaded by AdmiralMetalPrairieDog29
Matthew Nguyen
305606276
Discussion 1B
1.2
a. Subjects listened to 10 seconds of the Jackson 5’s song “ABC” and then were asked how
long they thought the song snippet lasted. Do people tend to overestimate the song length?
The observational units are the subjects listening to the 10 seconds of the song and the
variable is the estimation of the song length.
b.Are newborns from couples where both parents smoke less likely to be boys than newborns
from couples where neither parent smokes?
The observational units are the newborns and the variables are the gender of the
newborn and whether the parent smoked or not.
c. There are many diff erent types of diets, but do some work better than others? Is low-fat
better than low-carb or is some combination best? Researchers conducted a study involving
three popular diets: Atkins (very low carb), Zone (40:30:30 ratio of carbs, protein, fat), and
Ornish (low fat). They randomly assigned overweight women to one of the three diets. The 232
women who volunteered for the program were educated on their assigned diet and were
observed periodically as they stayed on the diet for a year. At the end of the year, the
researchers calculated the changes in body mass index for each woman and compared the
results across the three diets.
The observational units are women that volunteer and the variables are the change in
BMI and which diet the person was on
d. An instructor wants to investigate whether the color of paper (blue or green) on which an
exam is printed has an effect on students’ exam scores.
The students are th observational units while variables are the exam scores of each student and
what color they took it on.
e. Statistical evidence was used in the murder trial of Kristen Gilbert, a nurse who was accused
of killing patients. More than 1,000 eight-hour shifts were analyzed. Was the proportion of shifts
with a death substantially higher for the shifts that Gilbert worked?
The observational unit is the one individual 8 hour shift. The variables are whether any of the
patients died and if Kristen Gilbert wroked that shift.
P.1.8 Tennis players often spin a racquet to decide who serves first. The spun racquet can land
with the manufacturer’s label facing up or down. A reasonable question to investigate is whether
a spun tennis racquet is equally likely to land with the label facing up or down. (If the spun
racquet is equally likely to land with the label facing in either direction, we say that the spinning
process is fair.) Suppose that you gather data by spinning your tennis racquet 100 times, each
time recording whether it lands with the label facing up or down.
a. What are the observational units?
The tennis racquent
b. What is the variable?
Whether is landed it landed on facing up or down
c. Is the variable categorical or quantitative?
Quantitative
1. 10 In August of 2005, researchers for the American Society for Microbiology and the Soap
and Detergent Association monitored the behavior of more than 6,300 users of public
restrooms. Th ey observed people in public venues such as Turner Field in Atlanta and Grand
Central Station in New York City. For each person they kept track of the person’s sex and
whether or not the person washed his or her hands along with the person’s location.
a. Identify the observational units in this study.
The behavior of the users of public restrooms
b. Identify the three variables that were recorded on each observational units.
Person’s sex , whether they washed their hands, and the location
c. For the graph on the left , state a research question that can be addressed with the graph. Th
en answer the question based on the graph.
Does a person’s sex effect whether they wash their hands their not in a public restroom.
d. Repeat part (c) for the graph on the right.
Does the location of the public bathroom affect whether a user washes their hands or
not.
P.1.16 Suppose that the observational units in a statistical study are people who submit
information about themselves to an online dating service (think of match.com).
a. Identify two categorical variables that could be recorded for these people.
Two categorical variables could be the person’s gender and their location
b. Identify two quantitative variables that could be recorded for these people.
Two quantitative variables could be the person’s age and height
c. State two research questions that the dating service managers might want to investigate with
these data.
What age group is more likely to use a online dating service like match.com?
What city/area has the highest amount of online dating users?
P.2.2 Consider three students with the following distributions of 24 quiz scores:
a. Which student has the smallest standard deviation of quiz scores?
Amanda
b. Which student has the largest standard deviation of quiz scores?
Christina
P.2.6 Refer to Exercise P.2.5. Th e pair of P.2.6 dotplots displays data on the total number of
penalties called in the game, again separated by the type of referee. Summarize what these
reveal about whether the two types of referees diff er with regard to the distributions of this
variable.
Observing the two graphs provided we can make a logical conclusion that replacement
referee are more likely to hand out penalties.
P.3.5* Suppose that baseball Team A is better than baseball Team B. Team A is enough better
that it has a 23 probability of beating Team B in any one game, and this probability remains the
same for each game, regardless of the outcomes of previous games.
a. Explain what it means to say that Team A has a 2/ 3 probability of beating Team B in any one
game.
In any one game team A is more likely to win than team B as Team A wins 66.66 of the
games
b. If Team A plays Team B for 3 games, is Team A guaranteed to win exactly twice?
No
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c. If Team A plays Team B for 30 games, is Team A guaranteed to win exactly 20 times?
No
d. If Team A plays Team B for 30 games, do you think it’s very likely that Team A will win exactly
20 times? Explain.
No It would be very likely for Team A to have a number of wins around 20 or even exactly
however that cannot be guaranteed. The probability of the outcome of Team A to have
exactly ⅔ of the wins is likely to increase if more games are played.