Question

A psychologist is interested in constructing a 95% 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. 66 of the 811 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible.

a. With 95% 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 811 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.

Answer 1

sample proportion () = 66/811 = 0.0814

sample size(n) = 811

z critical value for 95% confidence level, both tailed test be:-

a).the 95% confidence interval  of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain be:-

With 95% 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 0.0626 and 0.1002

b). If many groups of 811 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About 95 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 (100-95)=5 percent will not contain the true population proportion.

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