Exam (elaborations)

CONFIDENCE INTERVAL

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Course
MATH225N (MATH225N

Institution
MATH225N (MATH225N

The NWBC found that 16.5% of women-owned businesses did not pro- vide any employee ben- efits. What sample size could be 99% confident that the estimated (sam- ple) proportion is within 6 percentage points of the true population propor- tion? Question Suppose a market re- searcher wants to deter- ...

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Number of pages 122
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the nwbc found that 165 of women owned businesses did not pro vide any employee ben efits what sample size could be 99 confident that the estimated sam ple proportion is within 6 percentage p

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MATH225N (MATH225N
Education
MATH225N (MATH225N
Course
MATH225N (MATH225N

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Alta - Chapter 8 - Confidence Intervals - Part 2
Study online at https://quizlet.com/_8whnz8

Correct an-
The NWBC found that
swers:$254$254
16.5% of women-owned
businesses did not pro-
EBP = 6%. ±=0.01T . he
vide any employee ben-
z-score is found
efits. What sample size
0.012=0.005=z±2=2.576
could be 99% confident
n=(z±2)2p(Ù
2)(q2)EBP2
that the estimated (sam-
=(2.5762)(0.165)(0.835)0.0
ple) proportion is within
n=253.96
6 percentage points of
the true population propor-
Rounded up to 254 peo-
tion?
ple.
Correct an-
Question
swers:$752$752
Suppose a market re-
Given the information in
searcher wants to deter-
the question, EBP=0.03
mine the current percent-
since 3%=0.03 and z±2=-
age of online shoppers
z0.05=1.645 because the
who are males. How many
confidence level is 90%.
online shoppers should
The values of p2 and q2
the researcher survey in
are unknown, but using
order to be 90% confident
a value of 0.5 for p2 will
that the estimated (sam-
result in the largest pos-
ple) proportion is within 3
sible product of p2q2, and
percentage points of the
thus the largest possible n.

, Alta - Chapter 8 - Confidence Intervals - Part 2
Study online at https://quizlet.com/_8whnz8

If p2=0.5, then q2=1 0.5=
true population proportion Therefore,
of online shoppers who n=z2p2q2EBP2=1.6452(0.5
are males? Round the answer up to
z0.101.282z0.051.645z0.02th 5e1.9
ne6x0tzi0n.t0e1g2e.r32
to6z0
be.0052
5 Use the table of values sure the sample size is
above. Round only at the large enough. The sample
final step. should include 752 online
shoppers.
Question
A recent survey asked
1,379 top executives
about business trends. Answer Explanation
The surveyed showed that Correct answers: 0.77
23% want to strengthen in-
novation to capitalize on The value of q2 is:
new opportunities. What is 1 p2=1 0.23=0.77
the value of q2 as a deci-
mal? Round to the nearest
hundredth.
Correct
an-
swers:1$0.652$0.652 2$0
To form the sample pro-
portion, take the number

, Alta - Chapter 8 - Confidence Intervals - Part 2
Study online at https://quizlet.com/_8whnz8

of successes, and divide
it by n, the number of tri-
Question
als. In this scenario, the
Alice wants to estimate
number of successes is
the percentage of people
the number of people who
who own a mountain bike.
own a mountain bike, 150.
She surveys 230 individu-
The total number of peo-
als and finds that 150 own
ple surveyed was 230.
a mountain bike. What are
p2=xn=150230=0.652
the sample proportions for So, p2=0.652 is the sample
successes, p2, and failures,
proportion, which is the
q2?
point estimate of the pop-
Round your answers to
ulation proportion. Since
three decimal places.
p2+q2=1, we can solve for
q2.q2=1 p2=1 0.652=0.3
Correct
Using p2=0.652, q2=0.348,an-
and n=230, what is the swers:1$0.590$0.590 2$0
95% confidence interval We know n=230, p2=0.652
for the proportion of the and q2=0.348. Since
population who own a the confidence level is
mountain bike? 95%, ±=1 0.95=0.0a5n,d
±2=0.025T . he z-value for
Use the table of common z0.025 is 1.96.
z-scores above. Round EBP=(z±2)(-
p2q2n )=(1.96)((

, Alta - Chapter 8 - Confidence Intervals - Part 2
Study online at https://quizlet.com/_8whnz8

So we can write the
your answers to three dec-
confidence interval as
imal places.
(0.652 0.062,0.652+0.062
The procedure to find the
confidence interval for a
proportion is similar to that
for the population mean,
but the formulas are a bit
different. We are still look-
ing for a range of numbers,
written as: (point estimate
- margin of error, point es-
timate + margin of error),
The Parameters for a Con- with (point estimate - mar-
fidence Interval with a Pro- gin of error) as the lower
portion value and (point estimate
+ margin of error) as the
upper value of the confi-
dence interval.
Since we're looking for
a point estimate for the
true proportion and mar-
gin of error for proportions
here, instead of means,
the point estimate will be
the sample proportion, p2,

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