According to a study conducted by a statistical? organization, the proportion of
ID: 3067207 • Letter: A
Question
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
0.840.84.
Suppose that a random sample of
100100
people is obtained. Complete parts? (a) through? (e) below.
?(a) Suppose the random sample of
100100
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.?(b) Explain why the sample? proportion,
ModifyingAbove p with caretp?,
is a random variable. What is the source of the? variability??(c) Describe the sampling distribution of
ModifyingAbove p with caretp?,
the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.?(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
0.8787??
The probability that the proportion who are satisfied with the way things are going in their life exceeds
0.8787
is
Explanation / Answer
(a) The response here is qualitative which is "yes" or "no".
(b) Here sample proportion is a random variable as its value varies from 0 to 100 as it represents the number of successes.
(c) Here the sampling distribution of p is approximately normal. Which have mean value 0.84 and standard error of proportion = sqrt(0.84 * 0.16 / 100) = 0.03666
(d) Here
Pr(p^ > 0.87) = 1 - NORM (p^ < 0.87 ; 0.84 ; 0.03666)
Z = (0.87 - 0.84)/ 0.03666 = 0.8183
Pr(p^ > 0.87) = 1 - NORM (p^ < 0.87 ; 0.84 ; 0.03666) = 1 - Pr(Z < 0.8183) = 1 - 0.7934 = 0.2066
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