A psychologist is interested in constructing a 99% confidence interval for the proportion of people who accept the theory that a person's spirit is no

Kyran Hudson 2021-02-25 Answered
A psychologist is interested in constructing a 99% confidence interval for the proportion of people who accept the theory that a persons
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Nathalie Redfern
Answered 2021-02-26 Author has 99 answers
Step 1
Solution:
Let X be the number of people agreed with the theory and n be the sample number of people.
From the given information, X=68andn=702.
Step 2
The sample proportion is
p^=Xn
=68702
=0.0969
Step 3
The confidence level is 0.99.
1α=0.99
α=10.99
α=0.01
Then, the 99% confidence interval for the proportion of all people who accept the theory that a person’s spirit is no more than the complicated network of neurons in the brain is
p^±Zα2(p^(1p^)n)=0.0969±Z0.012(0.0969(10.0969)702)
0.0969±Z0.005(0.0969(10.0969)702)
0.0969±(2.58)(0.0969(10.0969)702) [using the excel function = NORM.INV(0.005, 0, 1)]
=0.0969±0.0288
=(0.09690.0288,0.0969+0.0288)
=(0.0681,0.1257)
Thus, with 99% confidence the proportion of all people who accept the theory that a person’s spirit is no more than the complicated network of neurons in the brain is between 0.0681 and 0.1257.
Step 4
b)
If many groups of 702 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About 99 percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person’s spirit is no more than the complicated network of neurons in the brain and about 10099=1 percent will not contain the true population proportion.
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