SPA 3e_ Teachers Edition _ Ch 6
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L E S S O N 6.1 • What Is a Sampling Distribution? 405<br />
18/08/16 4:59 PMStarnes_<strong>3e</strong>_CH06_398-449_Final.indd 405<br />
d<br />
2. Would it be unusual to get a sample standard<br />
d d ddd deviation of s x 5 5°F or higher in a sample of size<br />
n 5 10 when s 5 3°F? Explain.<br />
d dddd d d<br />
dd dddd ddddd d d d<br />
d dd ddddddddddddd dd d<br />
d dd ddddddddddddddddd dd<br />
ddddddddddddddddddddddddddddddddd<br />
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0<br />
Sample standard deviation of temperature (°F)<br />
Lesson 6.1<br />
3. Based on your answer to Question 2, is there convincing<br />
evidence that the thermometer is more<br />
variable than the manufacturer claims? Explain.<br />
WhAT DiD y o U LeA rn?<br />
LEARNINg TARgET EXAMPLES EXERCISES<br />
Distinguish between a parameter and a statistic. p. 401 1–4<br />
Create a sampling distribution using all possible samples from a small<br />
population.<br />
Use the sampling distribution of a statistic to evaluate a claim about a<br />
parameter.<br />
Exercises<br />
Mastering Concepts and Skills<br />
For Exercises 1–4, identify the population, the parameter,<br />
the sample, and the statistic in each setting.<br />
1. Smoking and height<br />
(a) From a large group of people who signed a card<br />
saying they intended to quit smoking, a random<br />
sample of 1000 people was selected. It turned out<br />
that 210 (21%) of the sampled individuals had not<br />
smoked over the past 6 months.<br />
(b) A pediatrician wants to know the 75th percentile<br />
for the distribution of heights of 10-year-old boys,<br />
so she selects a sample of 50 10-year-old male<br />
patients and calculates that the 75th percentile in<br />
the sample is 56 inches.<br />
2. Unemployment and gas prices<br />
(a) Each month, the Current Population Survey<br />
interviews a random sample of individuals in<br />
about 60,000 U.S. households. One of its goals<br />
is to estimate the national unemployment rate. In<br />
January 2015, 5.7% of those interviewed were<br />
unemployed.<br />
(b) How much do gasoline prices vary in a large<br />
city? To find out, a reporter records the price per<br />
gallon of regular unleaded gasoline at a random<br />
sample of 10 gas stations in the city on the same day.<br />
pg 401<br />
Lesson 6.1<br />
p. 402 5–8<br />
p. 403 9–12<br />
The range (Maximum – Minimum) of the prices in<br />
the sample is 25 cents.<br />
3. Tea and screening<br />
(a) On Tuesday, the bottles of iced tea filled in a plant were<br />
supposed to contain an average of 20 ounces of iced<br />
tea. Quality-control inspectors sampled 50 bottles at<br />
random from the day’s production. These bottles contained<br />
an average of 19.6 ounces of iced tea.<br />
(b) On a New York–Denver flight, 8% of the 125 passengers<br />
were selected for random security screening<br />
before boarding. According to the Transportation<br />
Security Administration, 10% of passengers at this airport<br />
are supposed to be chosen for random screening.<br />
4. Bearings and thermostats<br />
(a) A production run of ball bearings is supposed to<br />
have a mean diameter of 2.5000 centimeters. An<br />
inspector chooses a random sample of 100 bearings<br />
from the container and calculates a mean diameter<br />
of 2.5009 centimeters.<br />
(b) During the winter months, Mrs. Starnes sets the thermostat<br />
at 50°F to prevent the pipes from freezing in<br />
her cabin. She wants to know how low the interior<br />
temperature gets. A digital thermometer records the<br />
indoor temperature at 20 randomly chosen times<br />
during a given day. The minimum reading is 38°F.<br />
Teaching Tip<br />
18/08/16 4:59 PM<br />
In part (a) of Exercise 3, the value of the<br />
parameter is not necessarily 20. It is a target<br />
the company is hoping to achieve, but it may<br />
not be the actual average number of ounces<br />
in the bottles. Likewise, in part (b), 10% may<br />
not be the true proportion of all passengers<br />
selected for a security screening, so it is not<br />
necessarily the actual parameter value.<br />
TRM Full Solutions to Lesson 6.1<br />
Exercises<br />
You can find the full solutions for this<br />
lesson by clicking on the link in the<br />
TE-book, logging into the Teacher’s<br />
Resource site, or accessing this resource<br />
on the TRFD.<br />
Answers to Lesson 6.1 Exercises<br />
1. (a) Population: All people who<br />
signed a card saying that they intend to<br />
quit smoking. Parameter: p 5 the true<br />
proportion of the population who quit<br />
smoking. Sample: A random sample<br />
of 1000 people who signed the cards.<br />
Statistic: The proportion of the sample<br />
who quit smoking; p^ 5 0.21.<br />
(b) Population: All 10-year-old boys.<br />
Parameter: The true 75th percentile of all<br />
10-year-old boys. Sample: Sample of 50<br />
patients. Statistic: The 75th percentile of<br />
the sample, 56 inches.<br />
2. (a) Population: Individuals in<br />
U.S. households. Parameter: p 5 true<br />
proportion of the U.S. population who<br />
are unemployed. Sample: A random<br />
sample of individuals from 60,000 U.S.<br />
households. Statistic: The proportion of<br />
the sample who were unemployed;<br />
p^ 5 0.057.<br />
(b) Population: All gasoline stations in<br />
a large city. Parameter: True range of<br />
gas prices at all gasoline stations in the<br />
city. Sample: A random sample of 10 gas<br />
stations in the city. Statistic: The range<br />
of prices in the sample; sample range 5<br />
25 cents.<br />
3. (a) Population: All bottles of iced tea<br />
filled in a plant on Tuesday. Parameter:<br />
m 5 the true mean amount of tea in the<br />
population. Sample: A random sample of<br />
50 bottles. Statistic: The mean amount of<br />
tea in the sample; x 5 19.6 ounces.<br />
(b) Population: All passengers in the<br />
airport. Parameter: p 5 the true proportion<br />
of the population who are chosen for<br />
random screening. Sample: The 125<br />
passengers on a New York-to-Denver flight.<br />
Statistic: The proportion of the sample<br />
selected for security screening; p^ 5 0.08.<br />
4. (a) Population: All ball bearings in<br />
the production run. Parameter: m 5 the<br />
true mean diameter in the population.<br />
Sample: A random sample of 100<br />
bearings. Statistic: The mean diameter in<br />
the sample; x 5 2.5009 cm.<br />
(b) Population: All possible times during<br />
the given day. Parameter: The true minimum<br />
temperature during the 24-hour period.<br />
Sample: The 20 randomly chosen times<br />
during the day. Statistic: The minimum<br />
temperature in the sample 5 38°F.<br />
Lesson 6.1<br />
L E S S O N 6.1 • What Is a Sampling Distribution? 405<br />
Starnes_<strong>3e</strong>_ATE_CH06_398-449_v3.indd 405<br />
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