According to a​ study, the proportion of people who are satisfied with the way things are going in their lives is 0.80. Suppose that a random sample of 100 people is obtained. Complete parts​ (a)...





According to a​ study, the proportion of people who are satisfied with the way things are going in their lives is
0.80.

Suppose that a random sample of
100

people is obtained. Complete parts​ (a) through​ (e) below.


Click here to view the standard normal distribution table (page 1).
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Click here to view the standard normal distribution table (page 2).
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​(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.


This is the correct answer.




B.


The response is qualitative 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.


Your answer is not correct.




D.


The response is quantitative 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.


Your answer is correct.




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



▼




than​ 5% of the population size and
​np(1−​p)=nothing≥​10,

the distribution of
p

is



▼


approximately normal

uniform

skewed right

skewed left




with
μp=nothing

and
σp=nothing.


​(Round to three decimal places as​ needed.)






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Jun 06, 2022
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