Deck 9: Estimation Using a Single Sample

Question 1

One difficulty in measuring the nesting success of birds is that the researchers must
count the number of eggs in the nest, which is disturbing to the parents. Even though
the researcher does not harm the birds, the flight of the bird might alert predators to
the presence of a nest. To see if researcher activity might degrade nesting success,
the nest survival of 102 nests that had their eggs counted, was recorded. Sixty-four of
these nests failed (meaning the parent abandoned the nest.)
Assuming that it is reasonable to regard the 102 nests in the sample as representative
of the population of nests for which the eggs have been counted, construct and
interpret a 95% confidence interval for the proportion of nests that have eggs counted
that are then abandoned.

Answer 1

We can be 95% confident that the true population proportion of abandoned nests is between 0.5336 and 0.7213.

Question 2

What is the interpretation of the margin of error?

Answer 2

The margin of error is the maximum error that is likely to occur when estimating a
parameter.

Question 3

is a biased estimator.

Answer 3

False

Question 4

What is the standard error of a statistic, and what information does it provide?

Question 5

A recent study investigated the effects of a "Buckle Up Your Toddlers" campaign to
get parents to use grocery cart seat belts. Investigators observed a representative
sample of parents at grocery stores in a large city, and found 192 out of 594 parents
buckling up their toddlers.

A) Compute an estimate of the population proportion of all parents who buckle up their toddlers
B) Based on the data above, what is the margin of error of ?

Question 6

is an estimator.

Question 7

All else being equal, the higher the confidence level, the wider the
confidence interval.

Question 8

In a couple sentences, define a "biased statistic" and "unbiased statistic." What is the
difference between the two?

Question 9

In a few sentences, identify the two desirable characteristics of a good estimator, and
explain what makes them desirable characteristics.

Question 10

In general, a wider confidence interval is associated with greater precision.

Question 11

An understanding of choices of habitat is an important element in understanding the biology and ecology of birds. One aspect of habitat choice is the pattern of preferred vertical height when feeding in forests. In a study of small birds in an old-growth forest in the Pacific Northwest, researchers, suspended from a giant crane, observed the landings of Golden-crowned kinglets (Regulus strapa). They found that 78 of the 163 landings were in the "mid" height region of trees, 21-40 meters above ground.

A) Compute an estimate of the population proportion of all landings of these kinglets that are in the 21-40 meter height range.
B) Based on the data above, what is the margin of error of \hat{p} ?

Question 12

What does the confidence level tell you about a confidence interval?

Question 13

For small samples, the margin of error is less than the standard error of

Question 14

The large sample confidence interval formula for estimating p can safely be used whenever

Question 15

The width of the confidence interval for p decreases as the sample size increases.

Question 16

A z of 1.96 is used when calculating 95% large-sample confidence intervals for p.

Question 17

Using an unbiased statistic guarantees that estimates will almost always be
close to the true value.

Question 18

Under what conditions is it reasonable to use the z confidence interval to estimate a population proportion?

Question 19

The margin of error of a statistic defines the minimum likely estimation
error.

Question 20

The standard error of

Question 21

When conducting research into the efficacy of drugs to combat psychological
disorders it is very common to use double blinding as a design strategy. In a double
blind study neither the patient nor the doctor knows whether the patient is receiving
the treatment or the placebo drug. Does double blinding actually work? That is, is
the doctor completely ignorant of the patient's assignment to their treatment group?
a) In a study involving the use of the drugs alprazolam and propranolol, 43 patients
with panic attack disorder and agoraphobia were treated. After completing the
study the physicians involved were asked to guess the treatments. The physicians
correctly guessed the treatments for 30 patients. Determine whether or not the
sample size is large enough to use the standard normal distribution to find the
margin of error. Be sure to show any supporting calculations.
In a different study of double-blinding, the use of lithium as a treatment to counteract
aggressive tendencies in adolescents was under study. In that study the physicians
correctly guessed the treatment in 37 out of 57 patients.
b) Assuming these adolescents and doctors to be representative, estimate the
population proportion of patients for whom the doctor could correctly guess the
treatment.
c) d) e)

Question 22

Under what conditions is it reasonable to use the z confidence interval to estimate a
population proportion?

Question 23

Briefly define the following terms in your own words:

A) Confidence interval
B) The confidence level associated with a confidence interval
C) The margin of error associated with a confidence interval

Question 24

Eyestrain is thought to be associated with different types of office work. The Acme Temp-Help Company provides short-term employees to substitute for vacationing data entry workers. Previous research has shown that approximately 21% of full time data entry workers have eyestrain, and Acme would like to estimate the proportion, p, of their 6,000 part-time data entry employees that have eyestrain.

A) They would like to estimate p to within 0.05 with 95% confidence. If they accept the value of 0.21 for full-time data entry workers as a reasonable initial estimate of p, what sample size should they use for their study?
B) Suppose Acme believed that the working conditions of their temporary data entry personnel are different enough that they should not depend on the 0.21 as an initial estimate. In a few sentences, explain how your procedure for choosing a samples size would differ from your solution in part (a). (Do NOT recalculate a new estimate of the necessary sample size!)

Question 25

Briefly define the following terms in your own words:
a) Confidence interval
b) The confidence level associated with a confidence interval
c) The margin of error associated with a confidence interval

Question 26

A newspaper recently conducted a survey of a random sample of 120 registered
voters in order to predict the winner of a local election. The Republican candidate
was preferred by 62 of the respondents.
Assuming that it is reasonable to regard the 120 voters in the sample as representative
of the population of voters, construct and interpret a 90% confidence interval for the
proportion of registered voters who prefer the Republican candidate.

Question 27

In a very large school district, student records have been kept in three distinct data bases, one each for elementary, middle, and high school. The district now has a new data base and wishes to correct any original data entry errors. To allocate enough secretarial time to this task, an estimate of the proportion of records that contain errors must be made. Initial estimates are that there are fixable errors in about 15% of the records.

A) Using 15% as an initial estimate of the percentage of records with errors, compute the sample size required to estimate the true proportion of records with errors within .025 with 95% confidence.
B) Suppose the school district did not have an initial estimate of p . In a few sentences, explain how your procedure for choosing a samples size would differ from your solution in part (a). (Do NOT recalculate a new estimate of the necessary sample size!)

Question 28

What does the confidence level tell you about a confidence interval?

Question 29

The choice of where to build nests is an important one for small bats. Their survival
and reproduction depends on making good choices. Research has suggested that the
warmth of the nest location is important, as well as protection from predators. In a
study of bats nesting under bridges over one and two lane roads in Louisiana,
researchers investigated the theory that nest location is affected by danger from
predators. The researchers reasoned that if bats were seeking to avoid predators they
would roost in the narrowest spaces available under the bridge.