Deck 10: Asking and Answering Questions About a Population Proportion

Question 1

The choice of the alternative hypothesis depends on the objectives of the
study.

Answer 1

True

Question 2

A statistic is a characteristic of a population.

Answer 2

False

Question 3

Answer 3

False

Question 4

Question 5

Question 6

Briefly address the following three questions about testing hypotheses.
a) Explain in your own words what a hypothesis test is.
b) Explain in your own words the distinction between a null hypothesis and an
alternative hypothesis.
c) What are the two possible conclusions when testing a hypothesis?

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Briefly address the following three questions about testing hypotheses.
a) Explain in your own words what a hypothesis test is.
b) Explain in your own words the distinction between a null hypothesis and
analternative hypothesis.
c) What are the two possible conclusions when testing a hypothesis?

Question 16

Question 17

A hypothesis test is only capable of demonstrating strong support for the
alternative hypothesis.

Question 18

Question 19

A Type II error is the error of rejecting a true null hypothesis.

Question 20

Question 21

Question 22

In an analysis of hunting by African lions, biologists filmed prey captures from the
safety of their vehicles. Prey captures were then divided into a sequence of events.
One of the events is the stalk, defined as the reduction of predator-prey distance for
prey that has been specifically targeted. The investigators identified two types of
stalk: (a) "crouching," -- the lion is concealed and either the lion advances toward the
prey or the prey advances (unaware) toward the lion, and (b) "running," -- the lion is
less concealed and advances toward the prey in a rapid manner.
Data on lions' stalks of wildebeests and zebras from a simple random sample of 159
kills are summarized in the table below. Researchers believe that the proportion of stalks that are the crouching type is about 0.87. Do the data above provide evidence that the researchers' belief is incorrect and
that the proportion of crouching stalks of wildebeests and zebras is different from 0.87?

Question 23

Question 24

Question 25

Assuming a random sample from a large population, for which of the following null
hypotheses and sample sizes is the large-sample z test appropriate? Show the
calculations leading to your responses.

Question 26

Question 27

Bats feed on insects at night and sleep during the day. Many species of bats use the
undersides of bridges for sleeping places. The beams that support a bridge create two
kinds of spaces in equal numbers: wide (approximately 55 cm) and narrow
(approximately 17 cm.) Biologists believe the bats choose narrow spaces to provide
more safety from predators. Investigators studying the sleeping position choices of
the Big-eared Bat (Corynorhinus rafinesquii) observed that 67 out of 102 of them
chose narrow beam spaces in which to sleep.
Does this sample provide sufficient evidence to conclude that the bats prefer narrow
over wide sleeping space? Use a significance level of .05 to test the appropriate
hypotheses.

Question 28

Question 29

Assuming a random sample from a large population, for which of the following null
hypotheses and sample sizes is the large-sample test appropriate? Show the
calculations leading to your responses.

Question 30

a) -0.65
b) -1.95

Question 31

Describe in a few sentences how each of the following affects the power of a
hypothesis test:
a) The size of the difference between the actual value and the hypothesized value of
the population proportion.
b) The significance level, α
c) The sample size

Question 32

A

Question 33

The field of pediatrics has consistently attracted a large number of women. To
balance their personal and professional lives, many women choose part time pediatric
positions. In the year 2000, it was estimated that 45% of female pediatricians worked
part time. Researchers would like to collect data in order to see if there is evidence
that this percentage has changed in the intervening years.
a) What null and alternate hypotheses should the investigators use? In a few
sentences, justify your choice of the alternative hypothesis
b) Describe a Type I error and a Type II error in this context.

Question 34

Question 35

Question 36

In an analysis of hunting by African lions, biologists filmed prey captures from the
safety of their vehicles. The capture of prey was divided into a sequence of events for
study, one of which is the stalk, defined as the reduction of predator-prey distance for
prey that has been specifically located and the prey is unaware of or minimally
alarmed by the predator. The investigators identified two types of stalk: (a)
"crouching," -- the lion is concealed and either the lion advances toward the prey or
the prey advances (unaware) toward the lion, and (b) "running," -- the lion is less
concealed and advances toward the prey in a rapid manner.
Data on lions' stalks of Thomson's and Grant's gazelles from a random sample of 151
kills is summarized in the table below. Researchers believe that the proportion of stalks that are the crouching type is about 0.87. Do the data above provide evidence that the researchers' belief is incorrect and
that the proportion of crouching stalks of Thomson's and Grant's gazelles is different
from 0.87?

Question 37

Hermit crabs fight for ownership of shells. Fights are initiated when one crab raps on
the shell of another with its big claw. An exchange of shells occurs approximately
50% of the time. Investigators wish to see if the rapping force helps decide the issue.
They set up an experiment with a rubberized shell, which would dampen the force of
the rapping. They reason that the reduced force should result in fewer exchanges of
shells. They then observed 59 fights to see how many shell exchanges occurred.
a) What null and alternative hypotheses should the investigators use? In a few
sentences, justify your choice of the alternative hypothesis
b) Describe a Type I error and a Type II error in this context.