Deck 11: Asking and Answering Questions About the Difference Between Two Population Proportions

Question 1

O

Answer 1

Question 2

Some animal behaviorists study the evolution of behavior as a consequence of natural
selection and the development of species. A common research question involves the
extent to which our human behavior is grounded in an evolutionary past, as opposed
to culturally imposed. For example, among monkey species in Africa males function
primarily as sentries, warning females that predators are in the area. Might it be so
that human males and females exhibit this behavior? That is, do human males
assume a protective role and human females a protected role? Researchers studied
the look-both-ways behavior of a random sample of males alone and an independent
random sample of males with females at a dangerous pedestrian crossing. They
reasoned that if males assume a protective role, they should look both ways at a
higher proportion when they are with females than when alone. The resulting data
are shown in the table below. a) What are the appropriate null and alternative hypotheses?
b) It is reasonable to use the large-sample test for a difference in population
proportions. Show that this is true by indicating the necessary calculations.
c) Test the hypothesis you indicated in part (a), and interpret your result in the
context of the study.

Answer 2

Question 3

Answer 3

False

Question 4

Question 5

Careful and constant and hygiene is necessary to reduce the chance of transmitting
pathogens by healthcare professionals. Despite the importance of hand hygiene,
getting good compliance is challenging. One complicating factor is the potential for
observer bias. That is, compliance monitors might be fellow workers who might
report higher compliance than neutral observers. A study designed to assess this
possibility was conducted in a hospital in a large city. Trained observers working
"under cover" - monitored hand hygiene compliance of a randomly selected sample
of healthcare professionals over a calendar year. Some observers worked in the same
hospital as the professional being observed (Unit-based) while others did not (Non-
Unit-based). Data from one of the hospital units are presented in the table below. Do
these data provide sufficient evidence of the existence of observer bias? a) What are the appropriate null and alternative hypotheses?
b) Show the necessary calculations to demonstrate it is reasonable to use the large-
sample test for a difference in population proportions for these data.
c) Test the hypothesis you indicated in part (a), and interpret the result in the context
of the study.

Question 6

One of the most striking human accomplishments is the achievement of intelligible
speech by age five. Males generally develop at a slower rate than females, and in a
recent large study of speech development in young children, investigators
hypothesized that a greater proportion of boys would have speech deficits for this
reason. Random samples of healthy two-year-old males and females were followed
over the course of a year, and at age 3 each child was classified as having a speech
deficit or not. The data are given in the table below: a) Construct a 95% confidence interval for the difference between the population
proportions of males and the proportion of females at this school who would be
classified as having a speech deficit.
b) Referring to your work in part (a), does there appear to be a difference between
the population proportions of males and females at this school who would be
classified as having a speech deficit? Provide statistical justification for your
answer.
c) Is this an observational study or an experiment? Justify your response in a few
sentences.

Question 7

Question 8

Some animal behaviorists study the evolution of behavior as a consequence of natural
selection and the development of species. A common research question involves the
extent to which our human behavior is grounded in an evolutionary past, as opposed
to culturally imposed. For example, among monkey species in Africa, males function
primarily as sentries, warning females that predators are in the area. Might it be so
that human males and females exhibit this behavior? That is, do human males
assume a protective role and human females a protected role? Researchers studied
the look-both-ways behavior of a random sample of females alone and an
independent random sample of females with males at a dangerous pedestrian
crossing. They reasoned that if females assume a protected role, they should look
both ways at a lower proportion when they are with males than when alone. The
resulting data are shown in the table below. a) What null and alternative hypotheses should the researchers test?
b) It is reasonable to use the large-sample test for a difference in population
proportions. Show that this is true by indicating the necessary calculations.
c) Test the hypothesis you indicated in part (a), and interpret the result in the context
of the study.

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

S

Question 15

Question 16

S c) Zero is included in the confidence interval.

Question 17

The pre-historic development of agriculture is an active area of research among
anthropologists. The transition from a hunter-gatherer society to an agricultural
society is generally assumed to be signaled by an increase in cavities in teeth.
Investigators recently studied teeth unearthed in two societies in Colorado:
Basketmakers, societies living in small villages, and Post-Basketmakers, societies
living in above-ground architectures such as pueblos. The investigators were
interested in whether the shift in shelter was associated with a shift in consumption
from hunting (meat) to agriculture (maize). Data on the numbers of individuals with
interproximal (between teeth) cavities are shown in the table below. Inter-proximal
cavities tend to occur more among populations subsisting primarily on agricultural
products. You may assume that it is reasonable to regard these two samples as
representative of teeth from these two populations. a) Construct and interpret a 90% confidence interval for the difference in population
proportions of individuals with interproximal cavities, Basketmaker - Post-
Basketmaker.
b) Interpret the 90% confidence level
c) Based on your results in parts (a) and (b), would you say that a shift in
consumption patterns is a reasonable conclusion on the part of the investigators?
Justify your response with statistical evidence from parts (a) and/or (b).

Question 18

Question 19

One method of human locomotion that appears to have no function except to express
joy is skipping, a skill usually learned in early and middle childhood. Each person in
a random sample of female students and a random sample of male students at a large
middle school was asked, "Approximately how long ago did you last spontaneously
skip?" The total sample sizes and the numbers who responded "Less than 1 week
ago" are given in the table below: b) Referring to your work in part (a), does there appear to be evidence of a difference
in the population proportions of males and females at this school who would
respond "Less than 1 week?" Provide appropriate statistical justification for your
answer.

Question 20

The pre-historic development of agriculture is an active area of research among
anthropologists. The transition from a hunter-gatherer society to an agricultural
society is generally assumed to be signaled by an increase in cavities in teeth.
Investigators recently studied teeth unearthed in two societies in Colorado:
Basketmakers, societies living in small villages, and Post-Basketmakers, societies
living in above-ground architectures such as pueblos. The investigators were
interested in whether the shift in shelter was associated with a shift in consumption
from hunting (meat) to agriculture (maize). Data on the numbers of individuals with
cavities are shown in the table below. Cavities tend to occur more among populations
subsisting primarily on agricultural products. You may assume that it is reasonable to
regard these two samples as representative of teeth from these two populations. a) Construct and interpret a 90% confidence interval for the difference in population
proportions of individuals with cavities, Basketmaker - Post-Basketmaker.
b) Interpret the 90% confidence level
c) Based on your results in parts (a) and (b), would you say that a shift in
consumption patterns is a reasonable conclusion on the part of the investigators?
Justify your response with statistical evidence from parts (a) and/or (b).

Question 21

Careful and constant and hygiene is necessary to reduce the chance of transmitting
pathogens by healthcare professionals. Despite the importance of hand hygiene,
getting good compliance is challenging. One complicating factor is the potential for
observer bias. That is, compliance monitors might be fellow workers who might
report higher compliance than neutral observers. A study designed to assess this
possibility was conducted in a hospital in a large city. Trained observers working
"under cover" - monitored hand hygiene compliance of a randomly selected sample
of healthcare professionals over a calendar year. Some observers worked in the same
hospital as the professional being observed (Unit-based) while others did not (Non-
Unit-based). Data from one of the hospital units are presented in the table below.
Do these data provide sufficient evidence of the existence of observer bias? a) What are the appropriate null and alternative hypotheses?
b) Show the necessary calculations to demonstrate it is reasonable to use the large-
sample test for a difference in population proportions for these data.
c) Test the hypothesis you indicated in part (a), and interpret your result in the
context of the study.

Question 22

Some psychologists hypothesize that a family history of speech communication
disorder might be a factor in speech delay. The theory is that if members of the
family have difficulty communicating, this may increase the probability of a speech
delay in a young family member. Random samples of healthy two-year-olds from
families with speech communication disorders and from families with no speech
communication disorder were followed over the course of a year. At age 3, each
child was classified as having a speech delay or not. These data are shown in the
table below: b) Referring to your work in part (a), does there appear to be a difference between
the population proportions of healthy two-year-olds from families with speech
communication disorders who have a speech delay and this proportion for those
from families without speech communication disorders? Provide statistical
justification for your answer.
c) Is this an observational study or an experiment? Justify your response in a few
sentences.