Chapter 22, Measuring Employment and Unemployment Video Solutions, Statistics

Problem 1

One month, there are $100,000$ people in the Current Population Survey
sample, of whom $63,000$ are employed and $4,000$ are unemployed.
$\begin{array}{l}{\text { (a) True or false, and explain: the Bureau would estimate the percentage of }} \\ {\text { the population who are unemployed as }}\end{array}$
$$\frac{4,000}{63,000+4,000} \times 100 \% \approx 6 \%$$
(b) What happened to the other 33, 000 people?

Oluwadamilola Ameobi

Numerade Educator

00:40

Problem 2

One month, there are $100,000$ people in the Current Population Survey
sample, and the Bureau estimates the unemployment rate as 6.0$\%$ or
false, and explain: the standard error for this percentage should be estimated
as follows-
$$SE for number=\sqrt{100,000} \times \sqrt{0.06 \times 0.94} \approx 75$$
$$SE for number=\frac{75}{100,000} \times 100 \% \approx 0.08 \text { of } 1 \%$$

Eleanor Archer

Numerade Educator

01:26

Problem 3

One month, the Current Population Survey sample is split into two indepen-
dent replicates. Using one replicate, the number of unemployed people is esti-
mated as 7.1 million. The other replicate produces an estimate of 6.9 million.
Using this information, estimate the number of unemployed people, and attach
a standard error to the estimate.

Justin Mathes

Numerade Educator

00:19

Problem 4

Using the data in exercise $3,$ what can you say about the bias in the estimate?

Eleanor Archer

Numerade Educator

00:34

Problem 5

A simple random sample is drawn at random $\longrightarrow$ replacement. Options:
with, without.

Nick Johnson

Numerade Educator

00:25

Problem 6

A box contains 250 tickets. Two people want to estimate the percentage of
l's in the box. They agree to use the percentage of $1^{\prime}$ 's in 100 draws made at
random from the box. Person A wants to draw with replacement; person B
wants to draw without replacement. Which procedure gives a more accurate
estimate? Or does it make any difference?

Eleanor Archer

Numerade Educator

07:12

Problem 7

(Hypothetical.) A survey organization draws a sample of 100 households from
$10,000$ in a certain town, by the following procedure. First, they divide the
town into 5 districts, with $2,000$ households each. Then they draw 2 districts
at random. Within each of the 2 selected districts, they draw 50 households at
random.
$$\begin{array}{l}{\text { (a) Is this a probability sample? }} \\ {\text { (b) Is this a simple random sample? }}\end{array}$$
Answer yes or no, and explain.

Jon Southam

Numerade Educator

00:35

Problem 8

A supermarket chain has to value its inventory at the end of every year, and
this is done on a sample basis. There is a master list of all the types of items
sold in the stores. Then, auditors take a sample of the items and go through the
shelves, finding the amounts in stock and prices for the sample items. To draw
the sample, the auditors start by choosing a number at random from 1 to $100 .$
Suppose this turns out to be $17 .$ The auditors take the 17th, 117th, 217th, $\dots$
items in the list for the sample. If the random number is $68,$ they take the 68 th,
168 th, 268 th, $\ldots$ items. And so forth.
$$\begin{array}{l}{\text { (a) Is this a probability sample? }} \\ {\text { (b) Is this a simple random sample? }}\end{array}$$
Answer yes or no, and explain.

Eleanor Archer

Numerade Educator

02:58

Problem 9

As part of a study on drinking, the attitudes of a sample of alcoholics are
assessed by interview.Cases are assigned to interviewers at random. Some
of the interviewers are teetotalers, others drink. Would you expect the two
groups of interviewers to reach similar conclusions? Answer yes or and
give reasons.

Mathew Botros

Montclair State University

03:12

Problem 10

From "The Grab Bag" by L. M. Boyd in the Soyd in the Soy Francisco Chronicle: "The
Law of Averages says that if you throw a pair of dice 100 times, the numbers
tossed will add up to just about $683 . "$ Is this right? Answer yes or no, and
explain.

Eleanor Archer

Numerade Educator

02:47

Problem 11

A polling organization takes a simple random sample of 750 voters from a
district with $18,000$ voters. In the sample, 405 voters are for. Fill in the blanks,
using the options below. Explain briefly,
$$\begin{array}{l}{\text { (a) The observed value of the $\longrightarrow$ }} \\ {\text { (b) The observed value of the $\longrightarrow$ }} \\ {\text { (c) The expected value of the $\longrightarrow$ is equal to $\longrightarrow$}}.\end{array}$$

Bryan Luo

Numerade Educator

02:49

Problem 12

In 2004 , there were $318,390$ applications to buy guns in California. IS $A$ crim-
inologist takes a simple random sample of 193 out of these applications, and
finds that only 2 were rejected. True or false, and explain:
$$\begin{array}{l}{\text { (a) } 2 \text { out of } 193 \text { is } 1.04 \% \text { . }} \\ {\text { (b) The SE on the } 1.04 \% \text { . }} \\ {\text { (c) } A 95 \% \text { -confidence interval for the percentage of all } 318,390 \text { applica- }} \\ {\text { tions that were rejected is } 1.04 \% \pm 1.46 \% .}\end{array}$$

Eleanor Archer

Numerade Educator