According to a study conducted by a statistical​ organization, the proportion of people who are satisfied with the way things are going in their lives is 0.88. Suppose that a random sample of 100 people is obtained. Complete parts​ (a) through​ (e) below. ​(a) Suppose the random sample of 100 people is​ asked, "Are you satisfied with the way things are going in your​ life?" Is the response to this question qualitative or​ quantitative? Explain.     A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.   B. The response is quantitative because the number of people satisfied can be counted.   C. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.   D. The response is qualitative because the number of people satisfied can be counted. ​(b) Explain why the sample​ proportion, p​, is a random variable. What is the source of the​ variability?     A. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully.   B. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.   C. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction.   D. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully. ​(c) Describe the sampling distribution of p​, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.   Since the sample size is ▼   no less no more than​ 5% of the population size and ​np(1−​p)=nothing≥​10, the distribution of p is ▼   skewed left uniform skewed right approximately normal with μp=nothing and σp=nothing. ​(Round to three decimal places as​ needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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According to a study conducted by a statistical​ organization, the proportion of people who are satisfied with the way things are going in their lives is
0.88.
Suppose that a random sample of
100
people is obtained. Complete parts​ (a) through​ (e) below.
​(a) Suppose the random sample of
100
people is​ asked, "Are you satisfied with the way things are going in your​ life?" Is the response to this question qualitative or​ quantitative? Explain.
 
 
A.
The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.
 
B.
The response is quantitative because the number of people satisfied can be counted.
 
C.
The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.
 
D.
The response is qualitative because the number of people satisfied can be counted.
​(b) Explain why the sample​ proportion,
p​,
is a random variable. What is the source of the​ variability?
 
 
A.
The sample proportion
p
is a random variable because the value of
p
represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully.
 
B.
The sample proportion
p
is a random variable because the value of
p
varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.
 
C.
The sample proportion
p
is a random variable because the value of
p
represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction.
 
D.
The sample proportion
p
is a random variable because the value of
p
varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully.
​(c) Describe the sampling distribution of
p​,
the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.
 
Since the sample size is
 
no less
no more
than​ 5% of the population size and
​np(1−​p)=nothing≥​10,
the distribution of
p
is
 
skewed left
uniform
skewed right
approximately normal
with
μp=nothing
and
σp=nothing.
​(Round to three decimal places as​ needed.)
​(d) In the sample obtained in part​ (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds
0.92​?
 
The probability that the proportion who are satisfied with the way things are going in their life exceeds
0.92
is
nothing.
​(Round to four decimal places as​ needed.)
​(e) Using the distribution from part​ (c), would it be unusual for a survey of 100 people to reveal that
80
or fewer people in the sample are satisfied with their​ lives?
 
The probability that
80
or fewer people in the sample are satisfied is
nothing​,
which
 
is not
is
unusual because this probability
 
is not
is
less than
 
0.05
0.5
5
50
​%.
​(Round to four decimal places as​ needed.)
 
 
According to a study conducted by a statistical organization, the proportion of people who are satisfied with the way things are going in their lives is 0.88. Suppose that a random sample of 100 people is obtained. Complete parts
(a) through (e) below.
(a) Suppose the random sample of 100 people is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain.
O A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.
O B. The response is quantitative because the number of people satisfied can be counted.
OC. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.
O D. The response is qualitative because the number of people satisfied can be counted,
(b) Explain why the sample proportion, p, is a random variable. What is the source of the variability?
O A. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully.
O B. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.
O C. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction.
O D. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully.
(c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.
Since the sample size is
V than 5% of the population size and np(1- p) =2 10, the distribution of p is
V with ua = and oa =
(Round to three decimal places as needed.)
(d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.92?
Transcribed Image Text:According to a study conducted by a statistical organization, the proportion of people who are satisfied with the way things are going in their lives is 0.88. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below. (a) Suppose the random sample of 100 people is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain. O A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not. O B. The response is quantitative because the number of people satisfied can be counted. OC. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not. O D. The response is qualitative because the number of people satisfied can be counted, (b) Explain why the sample proportion, p, is a random variable. What is the source of the variability? O A. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully. O B. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction. O C. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. O D. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully. (c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements. Since the sample size is V than 5% of the population size and np(1- p) =2 10, the distribution of p is V with ua = and oa = (Round to three decimal places as needed.) (d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.92?
According to a study conducted by a statistical organization, the proportion of people who are satisfied with the way things are going in their lives is 0.88. Suppose that a random sample of 100 people is obtained. Complete parts
(a) through (e) below.
O D. The response is qualitative because the number of people satisfied can be counted.
(b) Explain why the sample proportion, p, is a random variable. What is the source of the variability?
A. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully.
O B. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.
O C. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction.
O D. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully.
(c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.
Since the sample size is
v than 5% of the population size and np(1- p) = 2 10, the distribution of p is
with Ha =U and o
(Round to three decimal places as needed.)
(d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.92?
The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.92 is
(Round to four decimal places as needed.)
(e) Using the distribution from part (c), would it be unusual for a survey of 100 people to reveal that 80 or fewer people in the sample are satisfied with their lives?
The probability that 80 or fewer people in the sample are satisfied is, which
unusual because this probability
less than
V%.
(Round to four decimal places as needed.)
Transcribed Image Text:According to a study conducted by a statistical organization, the proportion of people who are satisfied with the way things are going in their lives is 0.88. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below. O D. The response is qualitative because the number of people satisfied can be counted. (b) Explain why the sample proportion, p, is a random variable. What is the source of the variability? A. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully. O B. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction. O C. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. O D. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully. (c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements. Since the sample size is v than 5% of the population size and np(1- p) = 2 10, the distribution of p is with Ha =U and o (Round to three decimal places as needed.) (d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.92? The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.92 is (Round to four decimal places as needed.) (e) Using the distribution from part (c), would it be unusual for a survey of 100 people to reveal that 80 or fewer people in the sample are satisfied with their lives? The probability that 80 or fewer people in the sample are satisfied is, which unusual because this probability less than V%. (Round to four decimal places as needed.)
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