Question

A psychologist is interested in constructing a 90% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 56 of the 833 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible. a. With 90% 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 and b. If many groups of 833 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About 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 percent will not contain the true population proportion. Hint: Hints

Answer 1

9 -833 x=56 = 56 0.067227 -0.6672 833 90%.CI -0.9 X=1-0.9 -0.1 Zolz=70.05 =1:645 90%. CI - P & 7012? $(1) 0.06723X (1-0.06723) 0.06723 + 10645 X $33 O 06723 t 1.645 x 0. 0086765 - 0.06723 t 0.01427 : 0.08150 0.05296 90%.CI - 0:0599 ; 0.0815

a. With 90% 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 0.0529 and 0.0815 b. If many groups of 833 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About 90 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 100-90 = 10 percent will not contain the true population proportion.