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. 74 of the 715 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 715 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

Answer:

a)

Given,

Here for 95% confidence interval,z score value is 1.96

sample size = n = 715

Estimated proportion = p^ = 74 / 715

p^ = 0.1035

Now 95% confidence interval = p^ +/- z*sqrt(p^(1-p^) / n)

substitute the known values in above expression

Interval = 0.1035 +/- 1.96*sqrt(0.1035(1 - 0.1035) / 715)

= 0.1035 +/- 0.0223

= (0.1035 - 0.0223 , 0.1035 + 0.0223)

= (0.0812 , 0.1258)

Interval = (0.0812 , 0.1258)

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 0.0812 and 0.1258

b)

If many groups of 715 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 5 percent will not contain the true population proportion.