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 0.72. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e below. O 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? O A. 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 B. 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 C. 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. O D. 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. (c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going 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 H. =and on =U (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 their life exceeds 0.75? The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.75 is (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 0.72. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e below. O 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? O A. 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 B. 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 C. 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. O D. 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. (c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going 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 H. =and on =U (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 their life exceeds 0.75? The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.75 is (Round to four decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 0.72. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e)
below.
...
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 varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.
В.
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.
C.
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.
O D.
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.
(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) = 2 10, the distribution of p is
with µa =
and on =
p
(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 0.75?
The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.75 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 64 or fewer people in the sample are satisfied with their lives?
The probability that 64 or fewer people in the sample are satisfied is , which
unusual because this probability
less than
%.
(Round to four decimal places as needed.)
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