SPA 3e_ Teachers Edition _ Ch 6

L E S S O N 6.1 • What Is a Sampling Distribution? 405
18/08/16 4:59 PMStarnes_3e_CH06_398-449_Final.indd 405
d
2. Would it be unusual to get a sample standard
d d ddd deviation of s x 5 5°F or higher in a sample of size
n 5 10 when s 5 3°F? Explain.
d dddd d d
dd dddd ddddd d d d
d dd ddddddddddddd dd d
d dd ddddddddddddddddd dd
ddddddddddddddddddddddddddddddddd
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Sample standard deviation of temperature (°F)
Lesson 6.1
3. Based on your answer to Question 2, is there convincing
evidence that the thermometer is more
variable than the manufacturer claims? Explain.
WhAT DiD y o U LeA rn?
LEARNINg TARgET EXAMPLES EXERCISES
Distinguish between a parameter and a statistic. p. 401 1–4
Create a sampling distribution using all possible samples from a small
population.
Use the sampling distribution of a statistic to evaluate a claim about a
parameter.
Exercises
Mastering Concepts and Skills
For Exercises 1–4, identify the population, the parameter,
the sample, and the statistic in each setting.
1. Smoking and height
(a) From a large group of people who signed a card
saying they intended to quit smoking, a random
sample of 1000 people was selected. It turned out
that 210 (21%) of the sampled individuals had not
smoked over the past 6 months.
(b) A pediatrician wants to know the 75th percentile
for the distribution of heights of 10-year-old boys,
so she selects a sample of 50 10-year-old male
patients and calculates that the 75th percentile in
the sample is 56 inches.
2. Unemployment and gas prices
(a) Each month, the Current Population Survey
interviews a random sample of individuals in
about 60,000 U.S. households. One of its goals
is to estimate the national unemployment rate. In
January 2015, 5.7% of those interviewed were
unemployed.
(b) How much do gasoline prices vary in a large
city? To find out, a reporter records the price per
gallon of regular unleaded gasoline at a random
sample of 10 gas stations in the city on the same day.
pg 401
Lesson 6.1
p. 402 5–8
p. 403 9–12
The range (Maximum – Minimum) of the prices in
the sample is 25 cents.
3. Tea and screening
(a) On Tuesday, the bottles of iced tea filled in a plant were
supposed to contain an average of 20 ounces of iced
tea. Quality-control inspectors sampled 50 bottles at
random from the day’s production. These bottles contained
an average of 19.6 ounces of iced tea.
(b) On a New York–Denver flight, 8% of the 125 passengers
were selected for random security screening
before boarding. According to the Transportation
Security Administration, 10% of passengers at this airport
are supposed to be chosen for random screening.
4. Bearings and thermostats
(a) A production run of ball bearings is supposed to
have a mean diameter of 2.5000 centimeters. An
inspector chooses a random sample of 100 bearings
from the container and calculates a mean diameter
of 2.5009 centimeters.
(b) During the winter months, Mrs. Starnes sets the thermostat
at 50°F to prevent the pipes from freezing in
her cabin. She wants to know how low the interior
temperature gets. A digital thermometer records the
indoor temperature at 20 randomly chosen times
during a given day. The minimum reading is 38°F.
Teaching Tip
18/08/16 4:59 PM
In part (a) of Exercise 3, the value of the
parameter is not necessarily 20. It is a target
the company is hoping to achieve, but it may
not be the actual average number of ounces
in the bottles. Likewise, in part (b), 10% may
not be the true proportion of all passengers
selected for a security screening, so it is not
necessarily the actual parameter value.
TRM Full Solutions to Lesson 6.1
Exercises
You can find the full solutions for this
lesson by clicking on the link in the
TE-book, logging into the Teacher’s
Resource site, or accessing this resource
on the TRFD.
Answers to Lesson 6.1 Exercises
1. (a) Population: All people who
signed a card saying that they intend to
quit smoking. Parameter: p 5 the true
proportion of the population who quit
smoking. Sample: A random sample
of 1000 people who signed the cards.
Statistic: The proportion of the sample
who quit smoking; p^ 5 0.21.
(b) Population: All 10-year-old boys.
Parameter: The true 75th percentile of all
10-year-old boys. Sample: Sample of 50
patients. Statistic: The 75th percentile of
the sample, 56 inches.
2. (a) Population: Individuals in
U.S. households. Parameter: p 5 true
proportion of the U.S. population who
are unemployed. Sample: A random
sample of individuals from 60,000 U.S.
households. Statistic: The proportion of
the sample who were unemployed;
p^ 5 0.057.
(b) Population: All gasoline stations in
a large city. Parameter: True range of
gas prices at all gasoline stations in the
city. Sample: A random sample of 10 gas
stations in the city. Statistic: The range
of prices in the sample; sample range 5
25 cents.
3. (a) Population: All bottles of iced tea
filled in a plant on Tuesday. Parameter:
m 5 the true mean amount of tea in the
population. Sample: A random sample of
50 bottles. Statistic: The mean amount of
tea in the sample; x 5 19.6 ounces.
(b) Population: All passengers in the
airport. Parameter: p 5 the true proportion
of the population who are chosen for
random screening. Sample: The 125
passengers on a New York-to-Denver flight.
Statistic: The proportion of the sample
selected for security screening; p^ 5 0.08.
4. (a) Population: All ball bearings in
the production run. Parameter: m 5 the
true mean diameter in the population.
Sample: A random sample of 100
bearings. Statistic: The mean diameter in
the sample; x 5 2.5009 cm.
(b) Population: All possible times during
the given day. Parameter: The true minimum
temperature during the 24-hour period.
Sample: The 20 randomly chosen times
during the day. Statistic: The minimum
temperature in the sample 5 38°F.
Lesson 6.1
L E S S O N 6.1 • What Is a Sampling Distribution? 405
Starnes_3e_ATE_CH06_398-449_v3.indd 405
11/01/17 3:53 PM